Any pistol with a second vertical grip is an AOW.

$200 for an individual to make a AOW, but a $5 transfer tax.
See if you can find a SOT to make your AOW tax free, then you only have to pay $5 transfer (plus thh SOT's fees)

Can give my SOT my 870, a 14" barrel, and a pistol grip, have him piece it together, and engrave his info on the receiver, then transfer it to me on a $5 stamp instead of a $200?

Couple things you have to do.  YOu have to supply him with an 870 that came factory-equipped as a PG-only shotgun.  YOu can't use a regular stocked 870 and make an AOW out of it.  YOu also can't possess the 14" barrel before you have an approved Form 1 or Form 4.

So, if you gave your SOT a PG-only shotgun, he could cut down the barrel to 14", or you could maybe order a 14" barrel and have it sent to the SOT (make extra sure they don't mess up the shipping and send it to the billing address for the CC, bad ju-ju).  He would install the 14" barrel, engrave his manufacturing info on it, register it on a Form 2 tax free and can then Form 4 it back to you.  He can even Form 4 it back to you if he is an out-of-state SOT, no need for an instate dealer to do the Form 4.  As long as he charges you less than $195, you are ahead of the game versus Form 1'ing it yourself for $200 and paying for your own engraving.

My SOT required me to ship him the PG-only shotgun in the original box with the label showing that it was a factory PG-only shotgun, model #24823.

There was some explanation below, but also keep in mind it needs to be an 07/02 SOT, one who can manufacture on a FORM2.   A typical SOT is just a dealer, and they'd have to do it on a FORM1 and spend $200 to do it.