I reverted my 1.10 game save to 1.9.1 by comparing the save file against an older quicksave from that game version, and removing anything suspect. The same process should work for 1.9.1 to 1.8.1. Satellites disappearing sounds like something changed in the way the data is stored on a part on those satellites between versions. In reverting 1.10 to 1.9.1 I had to rename the Poodle Engine Shroud from Shroud1 to Shroud, and remove the Comet Harvester references from any mining drills (among other things like flag mirror settings and removing comet celestial bodies.) You will also need to adjust the game version in the save file header.
Basically be familiar with what you have in your game in flight, and what was changed between 1.8.1 and 1.9.1 and adjust those references in the save file. Having a similar and recent 1.8.1 game save is important. My save file was 400k lines, so doing this requires a text editor that can diff files. Visual Studio Code, InteliJ (community), and atom should have the tooling required to walk through large files change by change and adjust them. I used IntelliJ in this case. This is somewhat tedious so ideally someone has a better option aside from this and 'next time back up your saves' and feels inspired to add to or correct this post with said potential better option.