Since this thread is back from the dead, I used to fry Crystal Castles to get unlimited lives. That only worked until you got extra life then it just plays like a regular game.
Here's two Solaris speedrun videos. While the player doesn't go to every sector, I suppose you can say he saves most of the the planets by finishing the game early.
Since you like Solaris so much, you could try The Last Starfighter, the prototype version of Solaris.
There was another bugged sector in the second part of the game. I recall it was a purple colored map and it had three minefields at the bottom of the map. In that one, I would destroy the fleets but not the minefields, leave to the right and save the planet there and comeback to the other map and the allied planet would be gone. As strange as this sounds, if I cleared the minefields as well as the fleets before I left the map, the planet is still there.
There is a tip I find useful, use a second joystick. That's because you can switch to the map while you're docked at a base, the game is paused. You can use this to save time and move faster.
Is it theoretically possible to beat Solaris without the loss of human life? (i.e. no planets have been destroyed by the Zylons)
I think it is. Although, my personal best was maybe nine allied planets saved.
I should also note that Solaris had some annoying bugs that could cost you a planet or two. For example, in the red sector with the allied planet on the upper right hand corner would sometimes get destroyed even you destroy all the fleets that threaten it. I mean I would destroy all the fleets, leave, come back a little later and find the planet gone and the sector's a red zone.
I did consider doing something similar if I ever got my hands on a Flashback 2 because I got a busted 2600. The idea of showing my friends that flashback with a working cart slot would've been fun.