I've got one of those, too!
Yours is a first generation, late 1950's, short framed KMZ (Dnepr) K-750. Rare, but still just a RPOC (Russian Piece-O'-Crap) at the end of the day. A lot of the parts are not original to the bike like the handlebars (originals were the cool ones with reverse mounted levers like CJ-750's), taillight/turn signals, 12v alternator (all K-750's had 6v generators), the endcaps on the cylinders, the rear fender (should be split/hinged) and fender supports (should be bowed), shocks, and maybe the rear swingarm. I think all that stuff probably came of a newer Dnepr MT-11 (except the SV endcap pieces!).
That's probaby why there's a big gap at the hockey puck/donut thingee. They probably used the shorter driveshaft from the MT-11 because the Dneprmatic gearbox is a little longer, thus requiring a shorter driveshaft. You can shoehorn a Dneprmatic gearbox in there (mine has one). They're much more reliable and are half-automatic (you really only have to use the clutch to put it into reverse because the shifter "pulls" the clutch for you!). Or since you're not going to be using reverse (I assume), maybe get one of the Dnepr 5-speed gearboxes that sacrifices reverse!!!
Before and after engine swaps...