Okay, I think I've got something that will work:
1. At the start of the first Activation phase of the game (after dials have been set, but before they have been revealed), before any other game effects occur, the players flip a coin, and the winner of the coin-toss gets a choice: (a) select the asteroid that will be moved this round, or (b) let the other player select.
2. The player chosen to select the asteroid now does so. The other player then places a 1 forward maneuver template somewhere in contact with the edge of the selected asteroid (using the maneuver template's short edge, long edge, corner, etc.). That player may then move the asteroid, with the option of rotating or flipping the token, and places it so that it is still in contact with the edge of the maneuver template but not overlapping any other asteroid, ship base, or the maneuver token, and remains within the boundaries of the play area.
3. The Activation phase resumes.
4. During the following round, the players do not flip a coin. Instead, they alternate between selecting and moving asteroids so that neither player selects or moves an asteroid on consecutive rounds.
Does that make sense?
Edit: The thread title should be "A house rule for mobile asteroids"
Edited by DagobahDave