Easy answer to the A2/A3 question: does it have a rear engine access door or not? If not, it's an A2. Yes, the dual-bank 6-71 is a really nice powerplant, but I bet there are a lot of parts made of pure unobtanium. It would, however, positively be a Marine machine, as I think only USMC got the A2 (because of shipboard concerns with gasoline and flammability).
I could immediately tell it wasn't an A4 because of the bogie spacing. The extra hull length is a dead giveaway. It's just as well, because the Chrysler multibank is the heaviest, least powerful, and hardest to work on of the bunch. They were all lend-lease as I understand it because the US Army didn't want the things.
It has the sharp-nosed diff housing (late) and VVSS with the high flotation end link mod (fairly late, or a depot job).
The Ford GAA is a great engine. The GM 6046 is a great engine. But there were a lot more GAAs made, and I bet it's a lot easier to rustle up a complete GAA than it is to find a complete GM 6046. That said, you only need 500 HP, so if you're having trouble hunting something down, just build a four-bolt-main big block Chevy and call it done, though you'd need a reducer box somewhere. The big block would be so much smaller and lighter than any other Sherman engine that there should be room for the reduction box in the engine compartment.
I really think this is a postwar rebuild of an A2 or an A3, or it's an oddity in being a M4A3(75)W or M4A2(75)W with hull applique armor over the dry stowage areas. The location and amount of applique armor really makes me think of a dry-stowage Sherman, but that's definitely a late (D78461) high-bustle turret with (I think) loader hatch and commander's vision cupola.
Hence my assumption that it's a postwar rebuild - they commonly put the (much better) late turrets on early hulls in the late 40s/early50s during the contractor and arsenal rebuilds. You'll know when you get a good look inside - if it has all the ammo storage down low in the hull in groups of six and four, and the water tanks are sealed up or removed, you have the postwar ammo racks. There should also be a data plate inside announcing a rebuild by Rock Island Arsenal, Kellogg Brown, or Bowen McLaughlin if nobody carried it off. There will also be hull numbers stamped a lot of places - try the front and rear towbar rings, near the rear corners of the hull, and inside near where the dataplate goes. You will probably need a wire brush - I bet there's a lot of paint on it.
To really nail it down we need higher res pics of the back of the tank - particularly down low around the exhaust pipe and engine access door area and the view down to the rear deck from on top of the turret.
Here is the best and most detailed page I've seen on identifying Shermans:
http://the.shadock.free.fr/sherman_minutia/index.html
M4A2 page:
http://the.shadock.free.fr/sherman_minutia/sherman_types/m4a2/m4a2.html
M4A3 page:
http://the.shadock.free.fr/sherman_minutia/sherman_types/m4a3/m4a3.html
Late M4A3 page:
http://the.shadock.free.fr/sherman_minutia/manufacturer/m4a375w/m4a3_75w.html
Turret ID page:
http://the.shadock.free.fr/sherman_minutia/turret_types/75mm_turrets.html
Postwar rebuilds:
http://the.shadock.free.fr/sherman_minutia/m4a3e4/m4a3e4.html
http://the.shadock.free.fr/sherman_minutia/mdap/mdap_tanks.html