When an 07/02 FFL/SOT Manufacturer makes an NFA weapon (MG, SBR, SBS, AOW, etc..) they register it with ATF on a tax free ATF Form 2. They pay a yearly fee to be licensed as a manufacturer. They do not pay a per gun tax when they make them.
So, if you can find one to do the work for you it would be as follows:
You buy a factory pistol gripped only shotgun from wherever.
You send it to an 07/02 FFL/SOT.
07/02 converts it to AOW at whatever cost he charges to do work.
07/02 registers the new AOW with ATF on Form 2.
07/02 then transfers it to you on a Form 4 for a $5 tax (assuming you are in the same state) + whatever he charges to do the transfer. If you are in a different state he would transfer it on a tax free Form 3 to a 01/03 FFL/SOT Dealer in your state who would then transfer it to you on a Form 4 for a $5 tax + whatever he charges to do the transfer.
Now, in my opinion the cheapest way to go would be buy an old 870 for $150, submit a Form 1 ($200 tax) to make it an SBS, once approved either buy a short barrel or chop yours. You can configure your SBS with a stock a pistol grip or any way you want. Here is my 870 14" SBS that I have about $575 in including the $200 Form 1 tax.