There are all sorts of AR-15 pistols out there that fit the description you have laid out.
The issues with removing the stock IMHO, The overall length of the gun has to be X inches with a Y inch barrel to conform to federal law. I believe X=26, and Y=18, but don't quote me. Removing the stock without extending the barrel moves you into SBR territory
The other concern I have is that once you change the firing position of the weapon, from something that was intended to be shoulder fired to something that could be interpreted as a handgun, you have opened a whole other can of worms.
If the lower has already been declared/constructed/transferred/sold as a rifle, and you start playing with lengths and configurations that could be deemed anything but a rifle under any definition, then you have another issue.
IANAL and this is way outside of what little knowledge I have on the subject, but tread lightly and watch out for constructive possession.