Hi Earl - Ha! I just went through this process with both the sink faucet and the shower fitting.
With the shower fitting, I had to cut an access hole like you did. Although you can almost reach it from the access hole behind the head, it was so corroded and hard to get the nuts off, I don't think it would be possible without cutting the access hole. I'm covering the hole with King Starboard (Seafoam color), which looks pretty good.
The head sink faucet was quite an endeavor too. When I lay on the floor and reach up through the hatch opening, the tip of my finger could barely touch the nut on the sink. But I couldn't see it at the same time, and other pipes and walls kept me from being able to swing a wrench. I ended up cutting the supply lines very close to the nut. So that I could slide a long socket over the nut. I needed a 1/2" ratchet with a 10" or longer extension to get the ratchet down where I could turn it.
As I recall, it was 1-1/8" socket to get the polybutylene nut off the supply line. Then it was a different size socket (I happened to have a 29mm socket) to get the nut off which fastens the faucet to the counter.
I felt very victorious when I finally got that bugger off. And I dropped several marine-grade curse words as I was contorting to get those nuts off.
I think that little hatch door under the head sink is quite silly, and it is also important because it is the access to 3 thru-hull valves. The door swings open in a way that blocks easy access and the whole thing was too darned small.
So I sawed a maximum sized hole where that hatch was, and I had a custom hatch made a boatoutfitters.com. It doesn't have a hinge, and just lifts out of the way for excellent access. I'm really happy with it. It is also made out of King Starboard (seafoam color).