I know I could do this in VBA, with a push button macro that would calculate based on parameters you set. I was looking at the solver setup. I think I have an idea how I could do it using that functionality as well. This looks like a really fun project, I'd like to make an attempt. Would you mind if I reformatted your player list so that each position was in a separate list? Believe having each position separated will make the logic easier to manage.
Is there a maximum number of players available in each position? Please message me if you want to discuss. I can complete this today.