Akai CD-93

How is Your progress, were You able to find a winding machine for the required wire diameter? I had to disassemble mine to find out reason behind cracks and pops (RCA shielding connection to frame wasn't done properly, and also found some other small issues on the servo/supply PCB-did I mention it was sold as "serviced"?). I also measured the sensor coil resistance (3065 Ohm) and also removed the connection on TR3 and it still works well-whatever reason is behind being fed this signal to the micom, it is now available again and works. Again I must say the sound of this player is fantastic.
 
removed the connection on TR3 and it still works well-whatever reason is behind being fed this signal to the micom,
Under normal operating condition TR3 sends a logic Low to the MCU when the pickup sled moves outwards and has reached a certain speed. To my understanding (I could be wrong) the MCU in turn switches the control gain of the sled servo by controlling TR2, connected at pin-7, in order to achieve certain control characteristics. And I think that would be the primary purpose for the L.M.I signal at pin-59.

When the sense coil fails, high out-of-spec impedance to open-circuit progressively, the machine would have difficulty loading a CD. It was accidentally discovered that by jumper TR3 base to GND the machine could be "tricked" to load a CD properly, and to play it if the sense coil hasn't gone "completely" bad, until it has gone "completely" bad. Obviously, with TR3 being forced always off the sled servo control characteristics would not be optimal.

When you have a good sense coil you do not need the jumper wire at TR3, and you did what you should by removing that jumper so as to recover the machine to its original state.
 
I think I figured out what is LMI: the CD mechanism is slanted when the loader tray is open. To ensure safe closure without trapping or damaging the OPU, the sled must be pulled inside and the tray movement must be disabled until sled reaches the center position. LMI signals the sled is still moving inward and in turn Tr2 pulls the SL0 output (slide motor driving signal output) to a certain dividing ratio by shorting one resistor, making lower movement speed inward (wich may have importance for the safety of the OPU) and also opens/keep open door until the sled moves to prevent accidental blocking of each other. When the sense coil is open, IC 10/1 will see a noise picked up by its inverting input that results some swinging on the output and so tray Loader will oscillate according to this signal.
 
There is a winding machine where I work but it's for much bigger power devices than the tiny coil in the Akai.

The person who uses it is on holiday now until next year so I don't know yet if they will be able to assist with rewinding my one.

I don't think they will be able to do much to help because it is so small and nothing like the large power transformers and coils they normally produce.