Man i have been waiting for this.....!

Why? Makes Zero sense.

If I want a 5.56 rifle, I buy a 5.56 rifle

If I want a 7.62 Rifle, I buy a 7.62 Rifle.

I would rather have 2 functioning guns than 1.5.
 
I'd rather start buying parts to what would eventually be something awesome like I've done with all my rifles the last several years. I wish I would have learned that lesson a long long time ago. That $300 would be a good start on a badass 5.56 AR. A high end barrel or high end upper or lower, down payment on a good scope, trigger... If you just want a small framed AR to shoot a lot and not be fancy then that $300 has you almost halfway to a beater AR. If you ask me, which I guess you didn't... They did you a favor not having it in stock. Put money into being able to shoot 5.56 in a heavy 308 platform? Don't do it.
 
I was just thinking about something like this the other day. The only reason I can see to put a 5.56 upper on a 308 lower is to run hand loads beyond "mag length" for a 5.56/223. Of course, you would also need a custom mag to accommodate the longer rounds. At $300, a mag well block to run a 223 lower with a standard magazine is pretty far fetched. Like was said above, you could buy a complete lower for that much.