MOHunter: I feel your pain....
In Wyoming, a good indicator if a unit has poor public access is available in the "Hunting Information and Regulations Booklet" (the annual regulation booklet). Areas that have difficult public access are clearly marked with an asterisk (*) right next to the unit number. I just looked up Unit 25 for antelope in the 2011 regulations, it has an asterisk by it. If you see the "asterisk" you know upfront it will be challenging to get hunting access. It's not to say it can't be done, but it will take a lot more work than on a unit with lots of public access.
You also mentioned that you are considering hunting elk in Unit 19. You might want to thoroughly check this area out for access as well. Unit 19 is also marked with an asterisk indicating difficult public access. It's not to say there is not hunting access in Unit 19, but it will be more challenging and really do your homework ahead of applying.
Another thing I have run in to over and over again when researching these "difficult to access" units. You might find a place to hunt, but in many of these areas, the elk know where the fence is for private land. As soon as the shooting starts, the elk move on to private in a hurry. Frustrated hunters end up seeing a lot of game, but in places they can't hunt.
Before applying for a unit indicated as "difficult public access", I would recommend getting a good map, such as the BLM map for the unit. Determine where you will actually be hunting. Make sure you have good access on "county" roads (not just any road). On a BLM map these "county" roads have county road numbers.
A general rule of thumb, if a unit is easy to draw, it usually has poor access, or poor hunting. Of course there are exceptions.