Look for an H-bridge motor driver. They are "reversible".
Plan is to write a sketch that controls the actuator, 2 ssr's to push out, 2 for inverted polarity to retract.
Unless you have a negative power supply available, it takes 4-contacts to switch polarity. (It can be done with a DPDT relay.)
What worries me (besides things that i may have overlooked) is that with inductive loads one should wire a diode into the circuit (see data sheet), but how to do that with reversable polarity ]
You might also have trouble with reverse voltage across a DC SSR. And, most AC SSRs wont work because they have a TRIAC and they can't turn-off with DC (after being turned-on).
I really haven't though about this so I could be wrong, but I assume an H-bridge works without a diode because when one pair of transistors/MOSFETs turns off, the other pair turns-on, providing a current-path for the reverse EMF.