Many of the guns in the AR/M16 family that start life out as a pistol have modified uppers & bolt carrier systems -- what does this mean? It means you can not use "regular" uppers on them. Gotta use their piece of crap upper. I haven't spent a lot of time looking at these, but I would wager that a registered DIAS is not going to work with one of those uppers. And it's not something as easy as dropping in a FA bolt carrier - the bolt carrier for the Olympic pistol is about 3" long. You'd have to be pretty good with the tools to turn it into an auto carrier. I agree with the other poster - get an AR15 and turn it into a SBR or put a short bbl on an M16. Experience has shown that you're going to have to tinker with the gas system on uppers shorter than 11" in order to get them to reliably function. Of course this isn't an issue with the 9mm uppers.
I have a 11" upper on my M16 and it runs like a champ. I also have a 7" (I think) DOE 9mm upper for my M16. Also runs like a champ. I tried a 7" .223 upper and could not get it to consistently empty a magazine on FA. Some folks have indicated that you could open up the gas port, which is located under the front sight post. Too techie for me, however. There was a wonderful write-up in Small Arms Review a few months ago that discussed the problems you could encounter with a bbl shorter than 11" -- essentially the article focused on the fact that the bullet doesn't stay *in* the bbl long enough after it passes the front gas port. The bullet leaves the bbl and the bulk of the gas escapes out the front of the bbl.
I'm running on, moral of the story is to buy an 11" upper and use that as the basis for your short bbl rifle. Going smaller than that length is a problem waiting to happen in the gas system.