Wait- do you have an IF-500 to go with your Tascam ATS-500?
I don't know those systems well enough to know if you needed an IF-500, like the MTS-1000 did with the IF-1000 in order to get transport control of a (or multiple) ATR's. If so, do you have a pinout for the cable that goes between the ATS-500 and IF-500, as I am told Tascam used (but never called out a part number in the MTS-1000 Manual) the same cable for their later series sync "pairs"?
My other option should this experiment with the Microlynx fail, is to try to get an IF-1000 to go with my MTS-1000, and at least run my Otari and MSR-16 together from the Tascam sync units.
I don't have the parallel interface or cables, unfortunately.
The original setup was locking two TSR-8s together, and the Lynx Mk1 didn't support TASCAM's serial protocol, at least not with either firmware version I have. I built some cables to try and make it work using the parallel (Accessory 1) port and telling the Lynx it was an 85-16, or Tascam 58 or something, but I never managed to get that setup going. With the ATS-500, it was using the Accessory-2 serial port, and after a bit of trial, error and realising that the schematics were wrong in the manual, I was able to make a set of cables to lock both machines together.
Eventually this became a hassle so I got an MSR-24, and got into a routine of recording the vocals and bass and anything else that needs a lot of punch-ins on the TSR-8, since the parts are cheaper. I record a MIDI guide track on the TSR-8, and when I'm happy I use the ATS-500 to lock the two machines together and transfer the vocals to the 24-track. The MSR-24 uses the same protocol which made things easier.
Finally I got an MX80 to replace the MSR-24. The Otari doesn't speak TASCAM's serial protocol, but the ATS500 it can do a code-only lock, so I roll the Otari first, and then get the TSR-8 to chase that.
IIRC the Lynx does support the MX70/MX80 so I could probably do this with the TASCAM as master, but what I have right now is working well enough so I've not really thought about changing it.
If you're using an MSR-16 and MTS-1000 the same option should apply - driving the MSR-16 direct via serial and locking it to an incoming timecode from the Otari.
It's worth noting that if you do the MSR-16 slave method, the capstan control line (i.e. the bit missing from the schematics) is supposed to be shielded. Mine wasn't, and as a result some of the values the ATS500 is showing are a bit unusual but it does work. Someone else had complete failure with the same setup until they had their cable remade with a shielded line for the capstan control. I may have got lucky.