If the dates on the 2009 Pueblo event are accurate, your event would be sandwiched between the Best Dam Barbeque in Boulder City, NV, already scheduled for May 22-23, 2009 and Pueblo. Both of those events are well established, KCBS and Boulder City is a Jack Daniel's "automatic" (assuming no new contests pop up in Nevada). Putting your contest in between those might not be the best idea. May is also the month that includes the Stagecoach Music Festival in Indio, CA which be another three day, two KCBS contest weekend and there is also the Modesto, CA contest that month. May is a tough month for a young contest to try and get a foothold.
Historically there is damn little going on contest-wise between mid-June and mid-August. I don't know what the weather is like in Silver City during that time period but that is the time window I would more strongly consider. If the weather is too hot that time of year, go for mid to late April as there isn't much going on then either.