I tried replacing the p-ch mosfets with n-ch mosfets today and I didn't get any substantial result. The n-ch mosfets start conducting without the charger connected, unless I dont connect Q10. If I do that then there would be no way the battery charger will start.
I think I am going back to my original design, p-ch mosfets in source follower configuration connected to a single n-ch mosfet inform a push pull arrangement. In theory, this should work but I just don't know why it isn't.
I have seen some complex models for lead-acid batteries. Have you Googled "lead-acid battery equivalent circuit modeling"?
I have used a large capacitor (farads) in series with a resistor (milliohms) and a high-value parallel resistor (for leakage or load) to test battery charger simulations. They worked well for me, but I never actually built the chargers and tested them.