Nice to see the old report come back to life.
All of the bikes you've mentioned would do fine on the roads in the the park. The heavy adventure bikes like the 1200GS, the Stroms, and the older Tigers can have problems coping with the sandy sections. Especially if you are there when the roads haven't been maintained in a while.
HERE is a trip I took out there on a '96 Tiger which convinced me look for a lighter dual sport. You really need to consider how much highway you plan to ride in your dual sport adventures. If you are hauling to where you are riding and just need a street legal bike to get between trail sections then I'd recommend that you go light. If you plan on riding the bike across country on the road to where you plan to ride some dirt roads then the heavier bikes are the way to go.