Looks to me like the relays are basically just switching pos and neg at the same time. Basically one is functioning in one polarity and the other is reversing the polarity to move the actuator the other way.
Just use two normal relays in place of each of the shown. Have one go to power and the other go to ground. Do the same thing with the other relay, just opposite.
Sorry I can't sit here and draw out a diagram for it right now, but if you don't get my drift reply to this and if i don't get to it in a while shoot me a PM to remind me and I'll try to get to it as soon as I can.