This is a question about setting up an AR with a scope, not which scope to get (I know that's a whole other huge topic). I want to set up my AR with a scope for 100m to 200m distances (that's the longest distance we have at our range). I currently have a Bushmaster XM15 with a 20" barrel. Now work with me on this, I'm a pistol person, and I may have some completely unworkable ideas about how to go about getting what I want, but here goes:

Can I get a "combat length" (16"?) upper with no carry handle, take the carry handle from my current upper and put it on that, then put a scope on my current upper? Is there a better way to do this?

I assume your 20" upper is an A3 with a removable carry handle.  You can remove the handle and add a mount, or add a carry handle mount to the upper as-is, and then add a scope.  No need for the 16" upper, unless you want one.

Not sure I fully understand your concern.

Ok, one thing I wasn't clear on is that I want to end up with two uppers (two guns would be nice, but $$), one scoped and one "combat". I just checked and the 20" does not have a removable carry handle, I assumed they all did. Thanks for that bit of direction. So, it looks like what I'll do at this point is put a scope on this one, mounted to the handle, and buy a shorty upper.

This has been covered a lot, but here's my .02:
you might find the 20" A2 style the worst of both worlds when it comes to scoping.  Obviously, you're limited to stuff that will be functional on the carry handle due to eye relief, etc; if you're looking for more than 4x or so, it might be difficult.  (I don't have this setup, I'm just going by memory from some pics I've seen here that folks have posted).  An ACOG might be your best bet here.  

You might be happier just getting another flattop upper, 16", then going to town on that one in terms of optics and mounts.  You won't lose any accuracy in the 16" gun at those distances (or any practical distance, really), and with a few $$ invested in some ARMS mounts, you can scope/red dot the new upper for distance AND CQB, and change the config with some quick throw levers.  

I have a 16" I call my Swiss Army Rifle.  It usually has an Aimpoint on it, but I can switch to a 3.8x12 scope in about 30 seconds...and then slip the bipod on there if I need it as well.  I've gotten 1/2 moa out of that rifle at 100 yards with handloads and the scope, so it does everything I'll need an AR type rifle to do.    

You might want to look into a cheekpiece also. I had a scope on my Colt and took it off because I wasn't getting a good cheek weld and wasn't satisfied with the way I was shooting with it. Took the scope off to preserve the "classic" look, and I shoot tighter groups with the iron sights. If you mount the scope on top of the carry handle (which is what I did) it just sits too high up, IMO.