AlliumCepa: For example a checker on the 8 point requires 2 moves. if you roll 6-5 each time you will need to use 2 5s at least, which is 10 on the dice to move 8 pips.

Better way would be to see how many moves each piece needs and make sure a maximum of 50% 6s are used.

So the 2 back checkers each need 4 moves (8 6s total)
The 5 checkers on 13 each need 3 moves (with no 6s needed)
The 3 checkers on 8 each need 2 moves (again, no 6s - 2 4s will do)
The 5 checkers on 6 could be moved out in 1 if 5 6s are used.

So,,, with 13 6s, 6 4s and 15 5s I could move them all out. That could be done with 13 6-5s and 4 5-4s (which would trade some 4s into 5s which is ok). Trading the 5-4s for 6-5s wouldn't help.

Thus 17 moves is the minimum with no doubles.