I have used a Roku device on an analog tv since 2013. I acquired a 2018 Roku Express+ to continue to stream my services, and it has worked very well, using an RCA cable. A few days a go I had to reconnect with Hulu, so I moved it to a higher resolution flat screen tv to input the password, using an HDMI cable. When I returned the device to the analog tv I couldn't activate it with the RCA cable. It still works and streams on the flat screen tv. I've tried unplugging to reset, but have not pushed the reset button.
Don't know if this will work but it can't hurt to try.
Put the Express+ back on the HD set. Go into Settings > Display type and change the Roku to the actual resolution of the problem tv. When you get to the countdown screen click on the "yes" option. Now move the Roku back to the first set and see if it works.