Reducing cost by eliminating microvias when designing a PCB with buried vias
An alternate way to save space is to use via-in-pad. If you aren't doing that already, it might save you enough space you won't need one of your two blind via types.

This was meant to be a flippant comment, since it technically answers the question, but doesn't really provide any new information. But the OP seems to think it's useful: 


  Q: Is there any way to route a signal from one side of the board to the
  other without at least one set of microvias?
  
  A: Yes, use a through via.