How safely to send signal between logic and higher current pcb?
I deal with exactly this situation on a regular basis.  Start by treating the ground connection at each pair of power boards as a star point for the power supply and controller board.  That is: relatively heavy wire between the ground terminals of both power boards.  Another wire from that point to the power supply ground.  One final wire from that point to the ground on the controller card.

What you want to avoid is having the load current cause a shift in ground potential between the logic board and the power boards.  The ground can (will) move around with respect to the power supply ground but so long as the signals between the control and power boards remain constant with respect to each other, you should be good.