The F710D was a 20 tooth 3/8" drive ratchet made from 1970 -78.
The " E " was for EXCHANGE , not 1944.
Snap On used to have a program where they would supply the drivers with rebuilt ratchets so they didn't have to rebuild them on the trucks.
You would give your driver your ratchet and he would exchange it for a rebuilt one .
When they rebuilt them at the factory they stamped an E on them for exchange.
The factory did not change it to 1/2" drive it must of been done by the owner or possibly he had his driver change it out for him.
Here are a few pics of an old F731 flex head that went through the exchange program.
Since it is two pieces they stamped both the head and the handle with an E.
Click pics to enlarge them.
The reason the kits your getting don't fit is because you must of been telling Snap On customer service that it was a 1/2" drive and they were trying to match you up to the right kit even though it is supposed to be 3/8" drive.
If you would of just gave them the part # they would of sent you the 3/8" rebuild kit RKRA38ALS.
You didn't say which kits were sent but I would guess that they sent you regular 1/2" drive kits and the gear in those is bigger than the 3/8" ratchet body so of course they wont fit.
Or they could of sent you the 1/2" in a 3/8" body rebuild kit # RKRASF730 mentioned above but that will not work as the gear is a little larger than those in the older 710 series ratchets.
You can rebuild it to 3/8" drive using the normal kit for it but you would need to get the right cover plate for it and they are not available from Snap On .
If you want to keep it as is and 1/2" drive the RKRA12DC kit should work for you.
If you were to send it in they would probably give you a 3/8" ratchet as they go by the part # on the tool.
If you decide to send it in keep the 1/2" cover plate as they are not available anymore.
I would just rebuild it and tell the guy at work to keep his hands off it or at least use a breaker bar and torch if need be.