You could do like many others do and build what they consider an AR pistol, and have as short of a barrel as you want on it, and no federal paperwork required.
The only difference in an AR pistol and an SBR is the stock.
If you have the plain pistol buffer tube on your lower, you are good to go, as long as there are no state or
local laws against owning one.
As long as you have a dedicated pistol lower, you can build or buy as short of a barrel upper as you want. You can't attach
a vertical grip to the handrail, or have any kind of shoulder stock or attachment that would act as a stock.
Some fellows build the AR pistol lower and have the short barrel upper of their choice, and later will go through the process of registering it as an SBR, if they want.
That way you can own and shoot a short barrel AR weapon
without all the federal paperwork.
It's not against the law to buy any short length AR barrel or
short barrel upper, as long as you don't attach it to a rifle AR
lower with a stock.
Just be sure that you have the pistol lower built before you build or buy a short barrel upper, if you have any other AR rifles in the house. The Fed's have intent laws, but as long as you have the pistol lower, you're legal.
As related to in an earlier post, you can go to,
www.ar15.com, where there is enough info. posted about
AR pistols, SBR's, and NFA rules, to give you a headache.