@Skydiver Thanks for the elaborate tests!
OK, that's good info and confirms my suspicion: Only sending Start/Stop Messages without clock are useless for the case at hand. I don't have nor know a device that solely responds to Start/Stop either. MIDI-Clock in usually relies on the clock signal and start/stop/continue/position are additional optional messages. Then again there may well be some MIDI device where this works.
The first 3 modes works as exactly they should (the 1 second delay in the' Clock + Transp + Pos" mode is also intentional ).
As for the case at hand, sadly the "Circuit"'s manual is not very elaborate. Page 52, 53, 62:
makes it sounds like it's either external-clock or not. It does not say if there are explicit messages to only start/stop the internal transport or how to control it.
There is another MIDI protocol: MMC (Midi Machine Control): Play, Fast Forward, Rewind, Record en/disable etc usually only supported by HDRs. Doubtful that the "Circuit" sequencer supports those, but it may.
Can you en/disable "buttons" using MIDI? Or MIDI-CC maybe? Might be worth checking what the "Circuit" sends out when you press play while it's using its internal clock.
Circuit output -> MIDI-cable -> Mac OSX -> https://www.snoize.com/MIDIMonitor
Maybe there's some dedicated circuit specific MIDI message...
 When seeking to a song-position, some HDRs need time to read files or wind tape.. so the plugin sends "start/continue", then waits for 1 second before starting the clock so that all slaved devices can be in sync. This hold-off delay is currently only configurable at compile-time.