It's not just about "opening up" other units. It's about being able to "guarantee" yourself a tag. If the OP can find a unit that he likes that has 100% draw odds based on last year's draw on a normal license, then I agree he should just do that. But most of the units that even have hard access are not 100% guaranteed draws on the normal license.
Bottom line, OP, look at last year's draw odds for the non resident random, circle all the units you could have gotten (ie units where there are more tags than first choice applicants), and see if any of those look good to you on the map in terms of access. If they do, you're done--apply for that unit. If not, look at the special random draw and go through the same exercise.
Go Hunt is NOT needed for this. Wyoming's draw odds page is good and accurate and with a little time, you can get all you need without paying any fees.