I may get some push back about this, but I ran machines for years like this in my garage.
The two wires from the single phase or house side of your system that are connected to L1 and L2 in your phase convertor, are the same ones you want to be connected to the R and S terminals in your machine that connect to the NC Transformer. This is the best way to do this. If you look closely in your rotary phase convertor cabinet, you may or may not be able to discern the true path of the two single phase wires after they leave the output side of the L1 and L2 connection block. I'm sure they head to the motor or capacitors, but there also may be a direct jumper from them to the output terminals of your phase convertor. If so, follow those and make sure they're what you use for R and S. That is if R and S are still connected as they are written in the manual. Though things look pretty messy in the bottom of your cabinet. Still connected as written could be doubtful.
I couldn't stand the sound of a phase convertor running while I was trying to think, so I put it in the basement remote controlled from the garage. I got the single phase power for the phase convertor off the sub-panel in the basement. Meaning all the machines in the garage were for all practical purposes, connected directly to the single phase system. I only brought back a single wire from the basement. Sometimes referred to and labeled as such as the Manufactured Leg by rotary phase people. This fed one rail in a 3 phase breaker box I had in the garage to feed the machines. You may be able to do something like this also.
Finally, pay attention to pumps of any kind on the machine and make sure they are turning the right direction. If not, swap R and S and no others to correct that. Many machines will turn the spindle in the proper direction regardless of how the thing is wired. Pumps and less intelligent motors don't have that luxury and need to be verified immediately on first time start up. If there is an oil pump supplying a reduction gear box or something like that and it's running backwards, it's going to have problems sooner then later. Typically if one pump is running properly they all are, but it never hurts to double check them all.
Not trying to be the barer of bad news, just hoping to help to get it done right.