I have more typically seen standoffs used to support boards, and some kind of board to board or other connector system in between. Can be 0.1" pin headers and sockets with the right dimensions to bridge the gap, or ribbon cables, or flat flexes, or specific high frequency connectors depending on the exact application...
If you are going to solder wires to each board as e.g. a cost saving measure (connectors can be expensive), perhaps dont double them up as supports, and keep them contained along one edge or in one area so that you can at least open the stack up if need be.
Soldering pins or supports between the boards to keep them separated and also route signals is going to make it a nightmare to probe and debug if required. Assembly and disassembly will be tough, and will eventually damage the boards if it has to be done more than a couple of times. So at least try to design your boards so that functionality is compartmentalised at the board level and they can be operated independently of each other for e.g. testing during manufacturing.