Use 0-5v+ to Switch 12v Relay

You can switch a relay with 5v yes. I would however look at the switching issue. If the switch will not activate a relay then its not going to activate your actuators that "suck". You have a problem with your switch if it wont activate a relay.  Your switch should not be giving you 5v output.

Try hooking up a pair of relays to the output of your module and eliminate the load of the actuators. See if the voltage drops when the module is running only the relays. The small load of the relays may make the voltage drop much less adverse than when its running the actuators. If thats the case, use the diagram in the door lock section of this site for reverse polarity actuators and wire your relays and actuators as it shows except instead of connecting the relays to an "alarm output" you will be connecting to your lock module. If your module is positive output you will need to change the fused +12V portion of that diagram to ground, and your 87A terminals to +12V. See what you come up with.

btw, those relays should switch fine quite a ways below 12V at a slight increase in amperage of course but at around 1/4 amp, an increase still wont be near the load of the actuators.