The standard USAF trash hauler is the E model ,with H's supplied when the major USAF contract finished.
The AC130A was the last of a long line of gunship try-outs during Vietnam
the others were the AC119G/K and of course the AC47 (Dakota not Chinook)
A turbo dak variant surfaced in the 80's in central america , but was converted in
limited numbers.
I have the Herk Bible by Col Lars Olausson and will check when the H's came on line.
The A's are still in service with AFRES and ANG units and will only be replaced by H's when the 'U Boats' come up to strength.
The J is another matter.
It is not in service as a gunship ,nor is it likely to be unless Lockheed sort out the
vibration problems caused by the engines.
Passengers cannot be seated fwd of the props due to filling loosening vibes on the stretched RAF aircraft .
I do not know how bad the short J is but it cannot be much better.
The H and U are very stable gun platforms , I do not know about the J.