Good clue. Now we have something. I'm not expert on the 230 but I know the 250. I think there is overlap with late 230. The FIP has a separate isolated oil supply around the centrifical govenor. That is what the dip stick and red cap are about. The pumps are, I think, given engine oil to keep gas from getting past the pumps. There should be a little pipe delivering oil to the piston area, I'm not sure how or if the oil flows through. On later models the oil spills out the front into the chain gallery.
I think the seal between the front and back has failed or the outlet is blocked. The engine oil is backing up into the govenor side.
The other symptom I read was the inconsistant idle as the FIP should easily adjust the idle. Check the manual on the FIP, I vaguely remember this type of issue but sorry, don't remember reading a solution. Since you have access to another but good running 230, pull the pump! Do a quick swap in with a known good device.
I also don't understand the extreme swings in a/f: I can see that on FT the FIP is dumpinf in gas. that can explain the rev limit, but then why does it swing to no gas with the motor reving from 3.5k to 4k. But I do like the dip at that point to near stoic at 4.6k, but then it startd dumping in gas again and the motor limits again. I do like the fact that it repeats. That gives us some focus. But it could be ignition with un burned fuel due to internittent/poor spark. Pull the other coil, then the disty, both pretty easy and quick.
I'd say pull the pump, sub in the good one. If the good pump fixes it. send the fip back to the rebuilder with history and ask for help. The engine oil in the regulator area is not correct on the 230 or 250.