That would be a good idea, except that now it's past the 90-day window (return attempt was in June, within the 90 days)
Just sharing my best-guess on this. You're right that it's probably NOT a good idea at this point to make a second return attempt just to be able to document it, because even if you weren't past the 90-day RP period, they would likely still look at it as an invalid claim because you have to attempt to return the item BEFORE you submit the claim, not after (in other words, it needs to be "I need to file a Return Protection claim for this item because I tried but I can't return it", not "I'm filing a Return Protection claim for this item and I'll attempt to return it if you ask me to").
I think you have two options at this point: If it's the type of retailer where you can contact someone who might take your word for it, you can call/e-mail/message them and ask for a letter stating that you did try to return it on XYZ date but that they wouldn't accept the return since it was outside of their ##-day return policy. (Remember to tell them that this is for an insurance claim, not for a dispute or chargeback that's going to affect them financially.) If they won't do that for you, then I would write a letter to AmEx Assurance simply stating that you called/e-mailed/messaged the retailer on ##/##/2024 and that while you unfortunately did not take note of the name of the person you spoke to (or the e-mail/message was answered by someone who did not provide their name), you were told that it was outside of the window for accepting returns, thus the return wasn't accepted by the retailer. I had to write a letter for a somewhat different situation--they were asking for proof of delivery but by that point they asked me for it, it had been more than 90 days since the purchase and eBay or Amazon no longer had the tracking number listed for the item--and I simply explained the situation and was approved. At that point, I wasn't too optimistic that it was going to get approved, but thankfully, it was. Anyhow, if you do decide to upload an explanatory letter, make sure you include whatever supporting documentation you can get--either a copy of the receipt where it shows the return policy, and/or a screenshot of their website where it states the return policy (assuming that they have a website...if it's a brick-and-mortar store and it's not too far, try getting a photo of their posted return policy maybe?). At some point, while of course AmEx Assurance is an insurance company, they're also serving us as AmEx customers so they'll hopefully take that into consideration and not treat you like they're investigating a multi-million-dollar health insurance claim or something like that.
I've also gotten the impression that the final approval--especially where additional documentation has been requested--all comes down to a subjective decision by whoever is assigned to your claim. Writing an explanatory letter might be enough for one claims adjustor but not another. Funny thing is, I've had a claim "closed" without payment because I didn't get around to submitting the documentation (but then even when it's "closed", you can still submit the documentation and they'll approve it, so "closed" is kind of a temporary status for RP). I also had a strange experience about six months ago where I had two claims that I didn't get around to submitting the extra requested documentation for (I think it was proof that I didn't return the item, or something like that), yet they STILL approved both claims a few weeks later! I wouldn't recommend taking that approach, but at least it's a DP (or two) attesting to the strange outcomes that sometimes happen with RP!