Richard,
Hi, again!
Follow he link in earlwb's post above. It describes your mystery engine very well as a 1960 type. With the center block separate from front and back ends, it is easy to swap the exhaust port from side to side. I doubt that the baffle piston would allow putting the exhaust to the rear- the six-bolt head wouldn't likely line up in any useful way.
To complete the swap, the piston and head would need to match the stock fit - baffle to the bypass side, head fitting on.
Also, if you are really adventurous, and if the front end bolt-pattern permits, you could reverse the rotation direction. Why? No idea, but it could be possible...
Remount the front end rotated 90° to either side. That makes up the needed 180° change. The intake is advanced or retarded 90° and meets the shaft port similarly advanced or retarded. However, the bias of port timing for high speed use would probably be reversed, defeating the purpose... Where the port opened early and closed late turning CCW, that could be reversed when turning CW.
Cheers to you , too...