With the 75 watt panel you have, I might be willing to chance it with the battery you have if it is a true deep cycle with something in the range of 80 AH capacity. If you're not sure of the battery, I'd bite the bullet and get 2 GC's.
You mention nat'l parks; Kissimmee Prairie Preserve State Park in Florida is a place to go to if you get a chance. I'm not an astronomy buff, but I do like the sky; this park is the only place where I've ever seen the sky as clearly as when I was at sea in the Navy. It was awesome!!
Doug