How do I correctly position two connectors that must be spaced precisely while soldering?
The easiest solution would be to provide a sample of the mating board for the assemblers to use to help position the connectors on your board.

You could make a custom board with the mating connectors, but then you have the problem of getting those connectors in the correct position to hold the connectors on your "real" board in the correct position to mate with the commercial board.  (then there's the question of how accurately the connectors on the commercial board are positioned - does the manufacturer expect the board to connect to another board, or just to cables?  If he expects cables, then there is little need for his connectors to be precisely positioned.)