I shot an nice buck in Unit 510 during the 2005 season. Plenty of goats around (pretty decent draw odds too) and gorgeous country (foothills of the Crazy Mountains). Though I can't really comment on the access as I applied for the unit because I met a friend from Big Timber who knew a few ranchers. I didn't have time to scout or hunt much, so I couldn't be too picky, yet I was able to show up in Big Timber at sunlight and be back in town by noon with a 13" goat in the pick-up. That was the one and only time I've hunted the unit so I don't know if my experience is typical or not. Though just by looking at the number of tags allotted in that unit and by giving a roadside eyeball test (lots of antelope are within eyesight of the highway), I'd say you have a very reasonable chance of drawing a tag and taking a nice buck in this unit. As far as, high end trophy quality, I have no idea of the unit's potential.
Here is a pic of that buck:
P.S. The only time I've heard of "paying a trespassing fee" to go on private land has involved out of staters who buy big ranches and lock everyone out. There should be plenty of Block Management, public, and private ranches that are more than willing to let you get rid of an antelope or two.