I think for some the fact that it continues without clock and adjust to changes in tempo is an interesting and useful and that’s why people don’t mind. Or at least it describes why I like Batumi. 
One thing, as a workaround or different logic, to perhaps try is:
Feed your clock to Batumi. Take the LFO out from batumi and put it into a gate. Control the gate with whatever you like. Feed the out of the gate to whatever you are modulating.
Then when you can keep the Batumi always clocked and not drifting, but drop the signal it is sending via the gate.
For example:
Set the Batumi in subdivisions mode and set LFO 1 to your 1/16th note tempo and LFO 2 to something much slower.
LFO1 square->Gate/VCA->Trigger something that is like a high hat.
LFO2 square->control the Gate/VCA
Now the high hat will play or drop out depending on the tempo of LFO2.
You could control that Gate/VCA with anything you like—force sensitive pad, another CV from your DAW, a random, an audio rate signal (be prepared for crazy results), etc.
Self-patching the batumi could also yield creative results here for LFO2.
I know the above isn’t exactly what you were after but is another way of thinking about these things that I mention because you noted that you are new to Eurorack and I want to make sure you see one of the ways that gates/VCAs get used to handle this kind of thing.
In general for Eurorack I have this mantra “the oscillator is eternal, we just choose how to release it.” In other words, there is no “starting” or “stopping” any oscillators, only choosing to let them out when we want them. It’s up to us to build a system that lets the oscillator out at the “right” moment. Stopping/starting is not the only state-change possibility, there is also open/close or covered/released.
