I guess your main issue is that generally oscillators in modular are free-running. And we generally don’t trigger the oscillator (to “start” it), but instead open some gate to clear the way for the already running oscillator signal to the next link in the chain. Whereever it is in its phase cycle.
I guess you would just need an oscillator that can reset its phase (restart its cycle) on demand. Which is effectively what oscillator sync is. Just syncing an oscillator with another will just have both cycles synced, but still free running. And keep syncing every cycle. You would need to reset it with a single pulse/gate.
Not sure at what point (at what voltage) the actual sync/restart would take place. Or more specific, if this is the same for all osc sync implementations.
For the Fundamental oscillator the documentation states: “The SYNC input applies hard-syncing to the waveforms by resetting the phase of the waveform when the sync signal passes upward through 0V”. So, I guess a pulse or gate signal would work just fine for that.
Maybe also read this thread about many things on Phase and Phase Shift
Maybe the Waveguide Delay (see the Phase shift thread) can give you access to any other then the initial/start phase angle (for basically any oscillator). Since with that you can introduce arbitrary delays with great precision.