"...then head out to Badger to get the permit, then to the trail head, try to be at camp by noon."
Guys, Badger Pass _is_ the trail head. The A-frame ranger station is next to the downhill ski area, and the trail head is at the top of the first row of the parking lot. That is also where the only permitted overnight parking is.
I don't think you are going to have much of a fire. For one thing, there is a bunch of snow on the ground, so twigs are going to be frozen and buried underneath that. You are not allowed to break anything off standing trees. So, the only good fire would be one that you carry in materials for. In the old days, we used to carry in a Pine Mountain Fire Log for that purpose. Actually, I think they make more light than heat.
When you start out from Badger, you go up the unplowed Glacier Point Road for about one mile. Then there is a trail going off to the left (uphill) that is a more advanced ski trail (the hill trail). If you continue out the road another quarter mile or so, there is another trail to the left(the meadow trail) that is much easier. The two trails merge a couple of miles out toward Dewey Point, and that is about where there is some tricky terrain. There is a killer view when you get all the way out there. I recommend that you do not camp directly at Dewey Point. For one thing, if any rangers come out there, they will be nosing around looking for violators of regulations. If you camp a little bit up the hill (west) from there, you will be out of the way a bit, yet you will be only two or three minutes from Dewey Point.