Alas, we are not going to be much help.
The f0 1c 70 1 60 messages are specific to H9control and thus are not documented.
For reasons which will now be obvious, they are only sent when H9control is connected to the H9.
Duplicating the H9control connection procedure would be difficult, and involves some secret sauce.
The H9 does not send a specific message when tempo changes, as it was thought that this would be handled by MIDIclock. The activity that you see is the H9 notifying H9control of parameter changes, etc.
I'm not familiar with "there’s this known H9 control communication loss problem when CLK.OUT is set to ON" – not known to me, alas.
I fear that MIDIclock will be your best bet. You can turn it off with a sysex message if you need it no more.
