As I have very few options as far as solenoids that will fit (either physically or my budget) I intend to not spend too much time calculating this force. I was hoping it was smaller than it is but now that I now what I am facing I intend to use the very last few thousandths of the plunger movement, where the force is the highest, and hope for the best. My valves are very big for the bore and only need open a very little distance.
I will have an operating (hopefully) example in a few days and will post pictures.