Joshua –
I took a closer look at your trip itinerary and don’t think you’re going to be able to hike the Highline trail at this time of year without either walking twenty-some miles to a low elevation spot or snow camping at either Granite Park or Fifty Mountain.
Glacier at the end of June is very, very snowy in the high country so you’re trip options are limited to valley walks perhaps broken up by a snowy crossing of a mountain pass back down to another valley in which you can camp again.
Consider this trip:
1. Start at Walton Ranger Station at the Southern tip of GNP. 2. Hike NE up the Park Creek drainage, camping at Lower and Upper Park Creek (seven mile days). 3. Cross snowy but safe Two Medicine Pass and camp at Cobalt Lake. 4. Exit the park at the Two Medicein area.
Another possibility would be:
1. Enter the park at Chief Mountain located in the NE part of the park and explore the Glenns, Cosley , Elizabeth and Helen Lakes areas. This would require an in-and-out hike with some backtracking on the same trails but it’s all low elevation . Or do a variation of that into just Glenns Lake and then day hike up to Stoney Indian Pass.
Other options would be rather than one five-day trip (which will be difficult to link up without lots of snow-travel) would be to do a couple shorter trips. For instance the one I suggested above as well as an overnighter to Cracker Lake from the Many Glacier area.
Mull these over using this (or another) map:
http://www.nps.gov/archive/glac/images/bigmap.gif
Feel free to ask questions about other sections of the park as well. I’ve been on 90% of the trails and I love talking about that place.