Really well worded situation you are experiencing.....sometimes pictures cannot add anymore.
I'm guessing you are now not in a position to turn off the booster switch and run the scan once again to see if the problem repeats itself. Took awhile before I too found out the booster should be off when using cable.
Maybe you could try disconnecting the cable, switch the box and TV back to antennae, run your scan, and see if the channels stay put when using this configuration.
Then repeat your complete install for cable and see what happens. I'm not sure where the command to revert back to channel 2 all the time comes from, but I suspect the TV has that feature imbedded somewhere. After all, when scanning, you're using the tuner from within the TV.
Not sure if that's any help.
Ken and Terry
2010 Georgetown 330TS being pushed by our
2017 GMC Terrain toad (4 wheels down)