The OP's reason for asking about turning the motor around is to get the wiring connections on the side giving cleaner installation. On electric motors and generators, the slang term for the wiring connection is the peckerhead. I have the same GE R-I motor on my camelback drill. The stator housing has the leads coming out one side of it. Without getting into the motor, from what I recall, the brush rigging and shorting bar are all mounted on the end bell casting. The bolt circles for both end bells look the same. The bolts are NOT thru bolts, but appear to be short bolts tapped into the flanges on the stator casting.
From the OP's photo, he had the motor apart to varnish the windings with Glyptal. If there is no difference in the end turns on the stator windings and the machining of the fits of the end bells & stator ends are interchangeable, the OP's idea is physically do-able. However, I am a mere mechanical engineer, and my electrical knowledge is very limited. Since the motor is an AC motor and there is no hard wiring between the brush rigging and the stator windings, it would seem that the OP's idea would work.
Looking at my old camelback drill (now partially buried for winter with a Lincoln engine driven welder hard against one side and a Harley close to the other side and a bunch more stuff wedged in), the peckerhead is on the LEFT side of the stator as you face the drive/shaft end of the motor. My own thoughts on the OP's motor are to "leave well enough alone". Some conduit fittings and conduit or "sealtite flex" will handle getting the wiring routed around the motor without risking any radical changes.
Years ago, on my first engineering job, I had to design some foundations for pumps. The year was 1972, and the field project super was an old timer who came up the hard way. I looked in a reference book for the NEMA frame details, and directed the electricials to stub up the conduits on the correct side of the foundations to line up with the peckerheads on the pump motors. The old project super was having none of that. He did not trust me or my reference book, and said he'd had too many jobs where the conduits were stubbed up on the wrong side of concrete foundations... conduit snaking around the back of a foundation to the get the peckerhead side of the motors looked like hell and he'd be damned if he'd take the chance on this job. He had me re-draw things and have the electricians bring the conduits up out of the concrete slabs on the rear end of each pump foundation, on the centerline of the motors/pumps. In that way, it would be a simple matter to swing the conduit down the correct side of the foundation, and it wouldn't look like a foul up. In the ensuing years of my career, I've had to deal with motors having peckerheads on the wrong side, going into existing locations (newer NEMA frames vs older frame series, or different types of motors). Sealtite flex and conduit and a little extra jog or two in the routing were what it took.