I decided to go with option #2 to start with, because it is a trivial matter (a single line of code) to switch to #1 later if it turns out that #2 wasn't the best solution.
This changes the game dynamic a bit in that it is now more difficult to get a high score, but in the long run, I do feel that this is best for the game.
The high scores have all been wiped, since they are no longer valid under the new version.