If the original "parent" gun had a shoulder stock on it at any time during it's existence, it would be considered a short barrel shotgun (SBS). This will cost you $200.00 to build on a Form 1, or to have transferred to you from an 03 FFL on a form 4. If it never had a shoulder stock (Mossberg JIC series, or other FACTORY pistol grip shotgun) or the build started from a bare receiver that had never been assembled into a firearm, it could be registered as an Any Other Weapon (AOW). That will also cost you $200.00 to build. If it is built by a 07 manufacturer it could be transferred to you on a form 4 for $5.00.
The only reason to go for an AOW vs a SBS if you are building it yourself
would be if your state doesn't allow SBSs but does allow AOWs. If you are purchasing an already assembled firearm, the transfer tax is cheaper for an AOW.
So, to answer your question,
can the stock on an existing gun be reshaped to a pistol grip?
Yes, for $200 dollars if you do the work yourself. OR For $200.00 + whatever the 07 manufacturer charges you to do the work.
The examples you gave asking whether they would be SBSs or AOWs . . .
sxs with 12" barrels like the one Mel Gibson had the Road Warrior
o+u with 12" barrels
and T/C Encore with a 12" 12ga. smooth barrel and pistol grip
Would depend on what the receiver was before it became what it is.
All things being equal, fat people use more soap. (I know I am one.
) High speed, low drag does not even come close to describing ME.