Simple solution, when you turn off the main TV with the HDMI connection, it turns off your box, if you turn your box on again, it turns the TV on.
Why not, when you turn your TV off and it switches your box off, whist your TV is in standby, turn the switch off at the plug socket, then turn the box back on. Watch it around the house as you like. Then, if you go to use the main TV again, just flick it on at the wall first, you would already be in the same room as the TV and the box. With the TV switched off at the mains, it can’t come on and interfere with the box until you want it to. Too many TVs, these days, do not have proper on/off switches, it makes me hope that my existing TVs go on forever, they can all be switched off properly.