Just went through the process to build a short barrelled AR. Not hard to do as long as your sheriff will sign off. Complete the paperwork, get fingerprinted, attach a photograph and send $200. The hardest part is the wait. Average seems to be 6 months but I got mine almost 5 months to the day.
You can buy a complete class 3 firearm from a class 3 dealer. You pay for the firearm, fill out and send the paperwork and wait. Once approved you can pick it up. I built my own AR. I filled out a Form 1 from the ATF (approval to manufacture a firearm). I had to register the lower receiver, put down the specs of the rifle I wanted to build and send in the paperwork/money. Since I was the "manufacturer" I had to have my name and town/state engraved on the receiver. While I waited I aquired all the parts I needed. I ordered a short barreled upper and kept it at my parents house until I received the stamp back giving me permission to build. I didn't want all of the parts at my house for the complete rifle until I got the stamp back. Now that the lower is registered as a short barreled rifle, I can order additional short uppers for the lower and swap whenever I feel like it as long as the rifle can be put back to the original specs on my paperwork. Sounds a little confusing but it's not that complicated. You cannot just get a class 3 permit and go out and buy a class 3 weapon. The "permit" is specific to each firearm. Do a search for NFA laws/procedures. That may help with any questions you may have.