That is an interesting challenge. I played around a little and tried to solve this situation as best as possible, but it is really tough to distribute the minutes sensibly. I think you have already come to some "good" conclusions too, but I would use a core 7-man rotation and use only 3 players for the third game of the week. Unfortunately, I was not able to find a perfect system, so you would have to sacrifice at least one player's game shape following this. Let's say you have Player 1 through Player 9 with 1-6 being your trainees. I came up wit the solution:
Game 1:
Starters_____________Backup
PG - Player #7________PG - Player #3
SG - Player #8________SG - Player #3
SF - Player #1______SF - Player #1
PF - Player #2______PF - Player #2C - Player #9_________C - Player #5
Game 2:
Starters_____________Backup
PG - Player #7________PG - Player #1
SG - Player #8________SG - Player #1
SF - Player #3______SF - Player #3
PF - Player #4______PF - Player #4C - Player #9_________C - Player #6
Game 3:
Starters_____________Backup
PG - N/A_____________PG - N/A
SG - Player #2________SG - Player #2
SF - Player #5______SF - Player #5
PF - Player #6______PF - Player #6C - N/A______________C - N/A
Now assuming you train 1v1 for forwards and that your starters get 38 min per game and backups 10 min respectively, then the minutes would be distributed as follows:
Player #1: 68 min

Player #2: 96 min

Player #3: 68 min

Player #4: 48 min

Player #5: 58 min

Player #6: 58 min

Player #7: 76 min

Player #8: 76 min

Player #9: 76 min

So you would definitely destroy the game shape of one player (Player #2), while one player (Player #4) is just shy of the amount of minutes needed. Here maybe a sports psychologist would come in just to somewhat lessen the effects of this ineffective distribution of minutes for these 2 players.
I'm looking forward to any other ideas from other managers, how a system could be effectively made for 6-trainee 9-man roster.