Planning Mammoth Cave Backpacking trip.

DW and I are going to a church-building mission trip in Somerset, KY during the first week in June. At the moment there are a ton of things unsettled about our travel plans. The 2 oldest one s are supposed to go with my DW's parents but we don't know for sure if they are taking the youngest. And we're not sure exactly which day the kid's are leaving (friday or Sat) or exactly what day we're supposed to be @ Somerset  (Sunday or Monday).  All this effects our trip planning, and it all could go out the window once we get to the visitor's cnter and try to get backcountry permits. So right now the plan is to do an overnight (or 2night) on the Good Spring Loop Trail saying at (atleast) one of the 4 campsites.

http://www.nps.gov/maca/planyourvisit/upload/BackcountryMap&Guide.pdf