Do you have points for antelope? One of the best units in the state is just NW of Baggs (57), bad draw odds though. Unit 52 is just east of your deer unit. Decent odds, nice goats and plenty of public. Any of the units around Baggs or the south central part of the state will be a tuff draw without the one point. 53 is good slightly below 50% draw odds on the special tag and good hunting with plenty of public. If you are willing to drive a couple of hours look at the late hunt in 48 and 47, should be an easy draw, good hunting and about 2 hours or so away, maybe a little more. The dates should match up with you deer hunt as well. If you are willing to pay a tresspass fee there was a guy in Rawlins that ran some hunts in several of the units around there that was reasonable and they killed some really nice goats and it is an easy draw for some of those units (56).
The guys company was called Out West Safaries, 307-324-9357. I never hunted with him, just looked at what he had. Hope this helps.