I don't think there were many (or any at all) M4A3 gun tanks in Normandy. The Large hatch M4A3s were produced too late to reach the front lines by that time. The small hatch M4A3s were used for Stateside training until a number were sent to the ETO as replacement tanks after the Bulge.
John, Thanks-- Yep, I'll have to adjust my timeline somewhat. But I've found photos of several small hatch M4A3s in France as early as July 1944, near Coutances, and some small hatch M4A3s before and after the BoB in Germany. I'm using "M4 Sherman at War", Kagero's "M4 Sherman", "Sherman in Action", along with Osprey's "Operation Cobra". But as a military researcher, I've learned not to always trust everything in print, and frankly there's a lot of incorrect stuff out there. Photo captions are always suspect to me, especially in modeling applications. As for replacements, the research I've done all agrees US Army tank units in the ETO sought to ensure the same types of tanks were in a single unit-- and since the Ford GAAengined M4A3 was the most numerous type produced, units were seeking to get some form of standardization to make re-supply and repair easier. The upshot of all this is that I really need the Sherman as a load for an M25/M15 "somewhere in France" (or Germany). I have in mind a double sided diorama-- the WWII Dragon Wagon with a "tank dozer" load on one side going in one direction, and Takom's new M1070/M1005 & D9R going in the other direction, as a comparison in size.
Don't rely on the captions in Squadron's old "Sherman in Action." The photos purportedly showing M4A3 dry stowage tanks do not show the engine deck or tail plate, nor the glacis, and it is unclear exactly why they were identified as M4A3's. Many of the telltale identifiers of the Ford production vehicles were not properly documented until much later.
The large number of M4A3's that appeared starting in late summer were brand new wet stowage tanks produced by Fisher. I have only seen five photos of dry stowage M4A3 tanks in Europe, and these were all rebuilds photographed in 1945. The Army did not send worn-out training vehicles overseas, unless they had been rebuilt, and the earliest photo of rebuilt M4A3's I have seen is dated to August, 1944. Given a four-month turnaround from factory floor to front lines, the earliest any of these would arrived in Europe is December, 1944.
From the rear, a dry-stowage M4A3 may be identified by the engine deck grills and the extended, flared-out, upper tail plate and exhaust louvers. From the front, the oversized cast radio pot on the glacis and the weld pattern around the drivers' hoods and the shape of the hoods' upper corners are distinctive. Pullman Standard M4's also had a large radio pot casting, but the driver's hoods were more rounded on the upper corners, and the castings did not meet on the vehicle centerline. The M4A3 hood castings, like those on the M4A4, were extended on the inner edges, so they met on the vehicle's centerline, and no insert was needed in between them. Obviously, a photo needs to be a reasonably close shot to make such distinctions.
A large cast radio pot and direct vision hood castings welded together along the vehicle centerline are a recognition point for early production M4A3 models. Small appliqué armor plates were welded over the vision ports during rebuild. Early and late models were rebuilt in no particular order, and were sent overseas as needed.
Other features sometimes seen on rebuilt M4A3's include fender extensions (to allow for duckbill tracks), and gun travel locks on the glacis. These were sometimes installed, sometimes not.
As for assignment of tanks by type, ideally a tank battalion would have only one type of engine, but the M4-equipped battalions eventually had to accept M4A3's as replacements, once the reserve stocks of M4 and M4A1 tanks ran out. In late 1944. the Army was short of tanks due to higher than expected loss rates, and re-equipping an entire battalion just for engine uniformity was out of the question, so repair teams had to stock both Continental and Ford engine parts.