@Donald I don't think you are ever going to get the NH Coating off enough to start fresh with a different type of formulation. I'm not certain what the base product is that NH Coatings uses but I'd want a similar type of coating if going the DIY route.
You'd need to pressure wash, scrub, use a bunch of degreasing chemicals/solvents, etc. You are going to create an oil slick on the floor if you do this in a garage. It will be a nasty job, I've been there. Plan on having a rubber squeegee to push the water out of the garage constantly. Then plan on washing the floors and driveway with soap when your done to clean things up.
I vote just take it to a local car wash and spray the underside as best as you can. Put it up on ramps and clean/degrease the areas by hand that still bother you. Let it dry and put a coating on that is compatible with the NH Coating stuff.
Use the Noxudol 700 in the cavities like inner fender cavities, engine bay nooks-and-crannies, inner door panels, rocker panels, etc.
I went from an oil base coating to Noxudol. Tremendous amount of work with pressure washing and drying.