Can't you just see the producer who says after the previews "Logan back with Stryker? That's depressing! Why don't we pay a little homage to the end of X1 where Mystique is playing Senator Kelly and add some post production effect to show it's really her?"

On a Watsonian level, Mystique working with Charles in this case would be the most sense making, yes. re: younger Erik's state of knowledge about Logan's powers, he didn't see them on display (solely the non-metal claws coming out in a fight), Logan just said they were both survivors. I suppose Erik could make an educated guess based on the fact Logan was the one sent back in time and on Logan not having permanently blood knuckles, but then again, he says "so much for being a survivor" when throwing Logan into a river, which would indicate he doesn't expect him at that point to come back. Mystique on her own has zilch idea about what's up with Logan, unless there's a missing scene they're saving for the dvd to explain it all. (I.e. a meeting between Mystique and Wolverine during this movie there he tells her something to intrigue her enough so she goes to the trouble of retrieving him.) Whereas one should think Charles would at least bother to wonder what the hell happened to Logan and to not want to see him on the bottom of the ocean, had access to Erik's thoughts again after Mystique took the helmet away and with the repaired state of relations could have asked Mystique to help getting Logan out of the river at least.

Why Stryker instead of impersonating random waterpolice cop: my fanwank would be that it has something to do with the newspaper article about Trask getting arrested for selling industrial secrets. I mean, that looks like a frame job to me, and playing Stryker would give her access to Trask in order to do it.

...but that's all awfully complicated and headache inducing. I maintain my Doylist theory is right.