The serial numbers on the barrel and receiver group are the same (see below). As noted earlier, the top of the barrel is marked "32-W." I've had the gun completely disassembled. All serial numbers I've found on the rifle are the same: Butt stock, fore arm, butt plate, barrel, receiver...I can't remember any more.
When I acquired the rifle (40 years ago or so) it was in very poor condition. Someone had attempted to improve that but did not have the skills nor the patience to do so and, accordingly had pretty much rendered it junk. I have restored every part. Accordingly, none of the external finish, except for the sights, is original. By the way, what kind of sights are these? They are wonderful. Many of the metal parts were badly rusted - some had been filed/sanded, the wood had been sanded and both were left (for many years) without finish.
The reason I asked for help with identifying the model number is that I keep having the same problems you have noted. It appears to be a "Number 3F - Fine Gallery rifle" which as you note "should be" a .22. Being a .32, it "should be" a " Number 2 Sporting rifle" but then it has the concave shape on the top of the receiver, and, from what I can tell, this rifle is radically different in other ways from a Number 2.
As mentioned before, the butt stock is rock hard tiger maple and the forearm is walnut. Again, both of these pieces have matching serial numbers stamped in them. Here's the butt stock as it is turning out. It's not quite finished.
Semper Fi and thanks for you interest.
DButt
USMC