I'm honestly surprised that I haven't done this idea already, but as far as I can tell, (unless I missed a chapter), I haven't, other than that one "traveling the various different anime universes with certain Bleach characters" idea. So this idea will seek to amend that.
This idea is based upon the truth that Alaya will send down counter guardians in times of need for humanity, and that during the original Avenger's movie, Archer gets sent down to help. For some mysterious reason, he's less forced by the counter force than usual, and he has more freedom over what he does and how he does it.
You can either have it so that by the end of the movie, Archer is sent back to the counter force, or you can have it so that he manages to stick around somehow via some method. Maybe Alaya thinks one of its counter guardians should keep an eye on the Avengers in case things go awry, as they do end up going in the civil war movie, or perhaps Archer forms a contract with someone in the Avengers to stay around longer, though I'm not sure Alaya would allow for that. Either way, Archer won't be cutting himself off from Alaya, so he will still be incredibly powerful due to Alaya's influence on him.
If you do choose the latter option, think carefully about who you choose, since that will heavily impact the story if you continue past the initial New York invasion. Whoever you choose, Archer will have to become entangled in all of their various adventures between the Avengers movies, since he's contracted to that person. If you choose Thor, he'll probably have to deal with everything in Asgard, and I'm not so sure how welcome he'd be there. It's definitely be the most unique choice, but I'm not sure if I'd recommend it or not.
Alternatively, if you have it be the former option where Alaya allows Archer to stay around to keep an eye on the Avengers, then you can give Archer go on his own "movies", or adventures throughout the Marvel universe. You can have other Marvel characters that aren't in the movies yet appear this way, and in general make the story your own. I want this Archer to be pre-UBW, so maybe have the "movies" focus on him building character via learning to not hate himself and to rely on others more. You can also have characters that are already in the movies appear, of course, if you want to do that.