It might just be less expensive to linen back every poster you own. Nice and flat that way.
That microchamber paper can get expensive. I use it on the comics I collect and they recommend 3 sheets per comic covering the whole page, One inside the front cover, one in the center and one inside the back cover. All cut to the size of the comic (I think CGC uses these in the comics they grade before finally sealing them). I don't know if a small sheet would protect a poster from a "non-acid neutral" foam core board. The microchamber paper is kind of used in comics (so I've heard) to help leach out and trap the gasses the paper releases and to help halt any further deterioration.
The comics also, get stored in Mylar and with an acid neutral board in each. So hopefully that collection of mine is as good as it will ever be.
It would be crazy to try to store each poster in Mylar. Just too expensive. Although that would help the flattening issue.
So maybe linen backing is your best bet after all (as long as you steer as far away from Posterfix as possible)?
Also, I've heard that some flat files have tops over the drawers to prevent papers from curling and getting caught when the drawers are opened and shut. (I can imagine this in my head as I've seen similar things on a smaller scale). So maybe you could just get some really thin plastic to lay across the top of the drawer in lieu of them having an "anti-curl" cover built in?
I am so going to build some of these in the near future. All of this flat file talk has got me hyped up about having a few for myself. And I can't wait to try to build them exactly how I imagine would benefit poster collectors.
Let's see... That will be #999 on my list of things to do now.
I can't wait to hear what you decided to do and how it all turns out! Good luck!