Somewhat random observations: Any Sugino JIS 118 axle should keep you in the ballpark you are in now. Sugino made many thousands of them. (But stay away from ISO. JIS and ISO are the tapers for the flats to fit the corresponding flats inside the cranks. JIS is the Japanese standard. ISO European. Campagnolo has a huge in fluence in the track racing scene so Sugino makes it track specific cranksets ISO to be compatible. Sugino 75 especially.)

If you choose to run the old axle again, try marine grease also known as boat trailer hub grease. I cannot explain why but I have successfully used bad cup and cone bearing for years with that stuff, paying zero attention to it.

While you have the BB apart, look the the cups. Are they OK or are they trashed? Typically they outlast the axles but bad axles will eventually take them down. If they are good, getting a new axle is a good move. If they are trashed, think new BB.

Shimano sealed BBs cost about $30, are bombproof, easy to install, are JIS and work well with Sugino cranks.

Ben