There are no save files, per se. The game execution files themselves are altered as you play the game. The reset and start over link just copies backups of the unaltered execution files over the current files.
If you want access to previous saves, you need to manually do the backups yourself, or use some of the bat files include in the STARFLT\PLAY folder (check out their contents to see what they do).
If you want to do the backups manually, then simply go to the STARFLT installation folder copy the entire PLAY folder to another location.
When you want to restore that "save" delete the PLAY folder, and copy your backup back to the STARFLT folder again.
You can keep as many backups as you want like this--just change the name of each backed up folder to remind yourself where you're at in the save.
Technically, you only need to copy the .COM files, but the whole folder's less than a Meg, so it's easy to just do the whole thing.