
I haven't read every detail here, but one thing I will comment on for consideration in regards to taking the main story as canon for your character's story is this:
Be cautious as you will eventually have everyone with your identical story, but don't write it off as entirely inappropriate. Creativity can get around most problems, especially depending on how you play the role. And when in doubt, talk it out. Get others' input, even if it's just "I would like to do ____ but don't want to do it in a way that comes off too over the top. Any ideas or suggestions?" Starting a dialogue can help.
My night elf hunter on WoW had a background where he wasn't directly involved in any of the main story of the past, but did cross paths with lore characters. I tried to avoid impacting them, but a discussion led me to feel it was still a bit too "Mary Sue" and it all shifted when someone said "Interacting with lore characters feels Mary Sue and honestly I find his mother defying tradition and training him in secret far more intriguing." So I dropped a lot and shifted his backstory to this far more meager and humble story that grew from there. Likewise to experienced RPers, be cautious with your advice. We can come off snobbish and abrasive, even when we're trying to help sometimes. =3
"Keep your words sweet...because you may have to eat them."
I'm only 17 on my pugilist, so I don't know all the details of the story, especially for the summoner, but I'll use WoW as an example, if I may.
My guild raided, when it was current content, Lady Vashj, Kael'thas, Illidan, Kel'thuzad, Malygos, Lich King, and Deathwing. That's 25 RPers killing 4 of those followed by about 20 (2 raids) killing Lich King and Deathwing.
For RP purposes, none of us took on the lore kill for Lady Vashj, Kael'thas, or Illidan. Some of us took on the lore kill for being involved in Kel'thuzad, though some said they were part of the assault on Naxxramas but not in the chamber for the battle with the lich himself while a handful of us were in the raid, but not involved with it for personal-canon since we were embroiled in the war against Malygos (hard to be actively fighting a war in one place and also actively involved in events of a different war somewhere else at the same time). And of the 20 or so of us, only one of our guild members was named (by the guild, not by the player) as being present for the actual defeat of the Lich King (and by lore, thus only that one player knew the truth of the events atop the citadel).
Despite fighting Deathwing for a few months, it wasn't until a massive group put together a full IC raid on Deathwing in LFR (easy mode makes for easier RP fights!) that we had our canonical assault that stopped him.
My point is to pick and choose your main story battles. If you're a summoner and you're going to incorporate Ifrit & Company (there's a band name for ya), I highly suggest trying to gather a group to do the full quest/encounter (other than the fight itself of course) in character. Immerse yourself in the details, the pain, and the struggle of those endeavors and think of the monumental effort it would take and the time you wouldn't be devoting ICly elsewhere in overcoming those tasks.
As someone else said, you will come out with a most epic tale of victory in how you were one of the few who accomplished this task and you'll be able to intertwine the tale with the other RP party members who journeyed with you and stood beside you! I think if you take 5,000 adventurers (server capacity ballpark) and we assume about 4500 of them are the nameless adventurers who are out there helping and keeping problems under control while the RP Coalition are the 500 remaining who are doing great deeds...and then even only a portion of them are taking the main story as their own, you do whittle down more and more towards those who have, by coalition canon, defeated the primals to be quite small.
That said, I would also encourage you to consider one other aspect. With fame and notoriety comes a great deal more problems. Do you really want to be known for these deeds and thus have every lord with coin expecting to have you do their bidding? To be asked constantly to save every little place from any little problem? Or would you wield this power more quietly and with discretion? I certainly wouldn't walk around town with a neon sign saying "I'm the Slayer of Primals" because that comes with the unspoken statement of
A: What problem may I resolve for you with my great power?
or
B: Come at me, bro.
Even if you do take Primal slaying as your canon, there are a lot of different ways you can play it afterwards as well. And if you choose discretion....what happens when your closest allies learn you've been keeping a secret or even lying to them about it? Things to think about for RP fun.
Be cautious as you will eventually have everyone with your identical story, but don't write it off as entirely inappropriate. Creativity can get around most problems, especially depending on how you play the role. And when in doubt, talk it out. Get others' input, even if it's just "I would like to do ____ but don't want to do it in a way that comes off too over the top. Any ideas or suggestions?" Starting a dialogue can help.
My night elf hunter on WoW had a background where he wasn't directly involved in any of the main story of the past, but did cross paths with lore characters. I tried to avoid impacting them, but a discussion led me to feel it was still a bit too "Mary Sue" and it all shifted when someone said "Interacting with lore characters feels Mary Sue and honestly I find his mother defying tradition and training him in secret far more intriguing." So I dropped a lot and shifted his backstory to this far more meager and humble story that grew from there. Likewise to experienced RPers, be cautious with your advice. We can come off snobbish and abrasive, even when we're trying to help sometimes. =3
"Keep your words sweet...because you may have to eat them."

I'm only 17 on my pugilist, so I don't know all the details of the story, especially for the summoner, but I'll use WoW as an example, if I may.
My guild raided, when it was current content, Lady Vashj, Kael'thas, Illidan, Kel'thuzad, Malygos, Lich King, and Deathwing. That's 25 RPers killing 4 of those followed by about 20 (2 raids) killing Lich King and Deathwing.
For RP purposes, none of us took on the lore kill for Lady Vashj, Kael'thas, or Illidan. Some of us took on the lore kill for being involved in Kel'thuzad, though some said they were part of the assault on Naxxramas but not in the chamber for the battle with the lich himself while a handful of us were in the raid, but not involved with it for personal-canon since we were embroiled in the war against Malygos (hard to be actively fighting a war in one place and also actively involved in events of a different war somewhere else at the same time). And of the 20 or so of us, only one of our guild members was named (by the guild, not by the player) as being present for the actual defeat of the Lich King (and by lore, thus only that one player knew the truth of the events atop the citadel).
Despite fighting Deathwing for a few months, it wasn't until a massive group put together a full IC raid on Deathwing in LFR (easy mode makes for easier RP fights!) that we had our canonical assault that stopped him.
My point is to pick and choose your main story battles. If you're a summoner and you're going to incorporate Ifrit & Company (there's a band name for ya), I highly suggest trying to gather a group to do the full quest/encounter (other than the fight itself of course) in character. Immerse yourself in the details, the pain, and the struggle of those endeavors and think of the monumental effort it would take and the time you wouldn't be devoting ICly elsewhere in overcoming those tasks.
As someone else said, you will come out with a most epic tale of victory in how you were one of the few who accomplished this task and you'll be able to intertwine the tale with the other RP party members who journeyed with you and stood beside you! I think if you take 5,000 adventurers (server capacity ballpark) and we assume about 4500 of them are the nameless adventurers who are out there helping and keeping problems under control while the RP Coalition are the 500 remaining who are doing great deeds...and then even only a portion of them are taking the main story as their own, you do whittle down more and more towards those who have, by coalition canon, defeated the primals to be quite small.
That said, I would also encourage you to consider one other aspect. With fame and notoriety comes a great deal more problems. Do you really want to be known for these deeds and thus have every lord with coin expecting to have you do their bidding? To be asked constantly to save every little place from any little problem? Or would you wield this power more quietly and with discretion? I certainly wouldn't walk around town with a neon sign saying "I'm the Slayer of Primals" because that comes with the unspoken statement of
A: What problem may I resolve for you with my great power?
or
B: Come at me, bro.
Even if you do take Primal slaying as your canon, there are a lot of different ways you can play it afterwards as well. And if you choose discretion....what happens when your closest allies learn you've been keeping a secret or even lying to them about it? Things to think about for RP fun.