You are right about having until 4:30 to pick up your permit. That was a change I didn't realize. The old way was that if you didn't pick it up by 10:00, then it was canceled so someone could use your first night (and the rest of the itinerary). Now since it isn't canceled until the end of the day, no one can use the first night (and probably much of the rest of the trip). I wonder what the reasoning was for this.
We were fortunate that we were able to prearrange a car switch. A group was going in Kintla the day we were going out so we shuttled their vehicle back to Bowman where we picked up our car.
Lake Francis (FRA) is between Brown Pass and Waterton (about three miles from the former and six miles from the latter). It is off the main trail about 1/3 mile if I recall correctly.
Here is a picture of Lake Francis:
Ever been to the Woodlands Inn? We stayed there over the holidays a few years ago.