David, I'll add my two cents worth. I've done a lot of operating in National and State parks and have found that there is no universal rule. You'd think there was, but there is not. So I have always operated with the 'most likely acceptable' approach. I'm like Glenn, I like mobile operating in a park. And if I do decide to operate on foot, which does happen, then I use the same approach as Glenn does on SOTA, super light, end fed, thin wire, QRP, cut to the band. This said, over the years I have also experimented with helium balloons, and even kites. They're fun, but lots of work and have their own down sides.
As far as what antenna I use when mobile operating in a park. I have three go-to setups.
Alpha Antennas FMJ mounted on my roof with a counterpoise for NVIS and a ground (when I have permission to put a ground stake (not 6-foot rod)). I usually ask first.
My favorite setup is an 80m doublet (so basically 138 feet tip to tip), strung from the tip of a SotaBeams 23-foot pole, that I mount onto the car hitch with a metal contraption I built to support it. (Next time I set up, maybe this weekend) I'll take detailed photos. Then comes the clincher. Usually I set up two more 23-foot poles at either end and set it up as a flat top. The problem is that those poles get staked into the ground. Now, because I said I like going for the safer route, recently I've developed a new approach. I set the doublet up as an inverted-V and use sandbags to hold the tips in place. Recently, a ranger came up to me and congratulated me on my no damage approach because, as mentioned, the center mast is off the ground (on my hitch) and the sand bags (the standard small striped kind) are inoffensive.
I have also developed a vertical approach on my 65-foot spider beam mast which also goes into my hitch. In this case, I use a 57-foot vertical wire and, if there is space, a full wave counterpoise that I roll out as needed based on the band.
Again, photos needed. I'll try to oblige.
Hope this was helpful.
Jim