Call the Buffalo field office of the Wyoming Fish and Game department and ask them to email you a list of landowners in units 23 and 24 (around Gillette and places just south, including the Thunder Basin National Grassland) who accept trespass fees from hunters. Start calling these people up.

Unit 23 may be undersubscribed, suggesting you ought to be able to draw a left over permit for a buck. Check the Wyoming Game and Fish web site for draw probabilities for Unit 23. Pay attention to how many permits are allocated versus how many permits were requested as first, second, and third choices. The difference is what is left over after the first drawing whose application deadline was March 15.

Note that generally there are not large heads available in the Gillette area. This doesn't matter to me, however, and I like the strong odds of drawing in this area.