The behaviour on the laptop screen is the same. I have uploaded the requested files
here. There are few differences, none involving RMbounds in RemoteMaster.properties and none at all in the .rmir files (after all I didn't change the remote configuration).
After further reflection, I think I understand what is happening. I didn't actually *resize* the RMIR window, so there is no reason why RMbounds should change. Instead, I simply maximize the window, which doesn't change the window size that Windows keeps for "Restore Down". Other programs, such as PSPad and Total Commander, remember the last state of the GUI in addition to the window size.
In my case I would be better served by an option "Always open maximized" than restoring the last saved window size. The stored window size won't be of much use when/if I change between screens with different resolutions.
Since I rarely use my laptop standalone anymore, I will simply change RMbounds to 0,0,1920,1080 manually in RemoteMaster.properties.
Problem solved!
Many thanks for your help!