My solution agrees with your findings:

$ perl min_steps.pl 3 7 11
5 steps:
   S->Y
   Y->Z
   Z->X
   S->Y
   Y->Z

$ perl min_supply.pl 3 7 11
Required supply: 11
6 steps:
   S->Y
   Y->Z
   Z->X
   X->S
   S->Y
   Y->Z
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