Hi guys. Thanks for all the replies! Maybe it is better just to modify the original circuit. Here is a picture and description.

I want to replace the DPDT switch with something controlled by a micro-controller. Maybe a ssr or logic level mosfet?

* Here is some functional info about the circuit : That section after the transformer with all the diodes and caps is just a rectifier area. The DPDT switch turns on the solenoid. That relay in the bottom right corner turns off K9 after a delay. This circuit gives the solenoid more power in the beginning to pull on and then less to hold it on. The gray oval components are just spark suppressors for switching large dc.

 

For that I calculate an end voltage across the solenoid of ≈56% of the supply voltage.
Where do you get 70%-80%?

Less than 50%, more than 50%, 56%, 70-80%.

I don't see anything definitive other than more seem to think it's more than 50% than less...