Cyndi and I figured out how the games are chosen, and made a little setup to help you get the games you want in Wii Fitness and to make the run less RNG:

1. Create a new Mii (or use a Mii that has not been registered in the player list, if you have one)
2. Do one Wii Fitness test with the new Mii (it will be the default games)
3. Play Working the Bag, Target Practice (Tennis), and Spin Control once (in training mode), in any order
4. Set the date forward one day
5. Do another Wii Fitness test with the new Mii (this will be the games you just played)
6. If you finish a run (the third game fades to black), you will need to do another default games run before you can play these three games again.

Note: You don't have to play the specific 3 games I mentioned in Step 3 (maybe you wanna test if a different game is faster), but one of them has to be a Boxing training game, or you will just get Returning Balls.

The reason this works is because when the fitness test games are randomized, the game will first pick the training games your current Mii has played. (This is why you need to use a fresh Mii.) If the current Mii has not played any games yet, it will default to Returning Balls, Hitting Home Runs, and Picking up Spares (in no particular order).

Then, the three games you played in your previous test are removed from the possible choices. If this is your first test, you will always get the 3 default games (this is why you need to play one test first, and why you need to do another test if you finish a run).

But yeah, the system clock has nothing to do with the game pool.