Is the "Run" button on the Rigol a real switch,or a virtual one?
If it is real,maybe it sends a loop,open,or some hard wired data signal to the rest of the 'scope's innards.
If it does,possibly the switch function itself could be duplicated & extended,without getting into the control system firmware.
I don't have a Rigol so I don't know if this is possible,plus I am an analog/hardware person,but several times over the years,in various jobs we have solved similar problems by this rather clunky & inelegant method.
VK6ZGO