Hi Aligator,
We've had really good luck with the Walk-Up Permit process. Both times we landed Hole and Frances as a latter night out (3rd, 4th or 5th). Would encourage you to take PeteE's advice regarding an early arrival at the Permit office if going for a WalkUp though. Brought my coffee, sleeping bag and fabric chair and cozied right up against the door, arriving about 4:30am (yeahhhh, little bit neurotic on that!) Pretty exhiliarating to land a great Walkup!
Like others have suggested, i think it really important to have multiple itineraries ready to go in your mind as you step up to see what's available at that moment. With 3 other offices opening at the same time to give Permits, you don't want to stall too long if your first choice gets taken. That's where Chat was really helpful in advance, to be able to read trip reports of other itineraries and scoop up ideas on sweet spots from the Pro's (just like what Joybird suggested). So many of those 'lesser thought of' campsites are at or near great locales. And a lesser desirable camp on Night #1 can be your open door to a fantastic weeklong itinerary.
E.g. Accepting Waterton or Goat Haunt Shelter as your 1st night for an itinerary eventually headed to Fifty and Stoney, or up to Boulder Pass.
We've yet to try Slide Lake as our 1st night to a trip in The Belly but numerous reports are that its a fine camp and great hiking up Lee Ridge to get to it.
With each of these alternatives however is the required logistics about your vehicle worked out in advanc. So our Walkups were likely going to be "Out and Back". That's actually not been a disappointment at all as the scenery looks anew on the return.
At our fingertips though, we had looked into logistics if we wanted to sign up for a ThruHike. I.E. the shuttle situation, which now is much more limited than in the past. We also talked to a taxi company that functioned out of Browning, The Mountain Chief Cab Company, and for a price they could provide transport to/from Chief Mtn. Don't really have any reviews however of the reliability of this service. We also questioned, if we came out at Chief, if we would have cell service there to be able to call for the Cab? Didn't know if the Border Crossing station might allow us access to a landline but doubted it. If going between Chief and Goat Haunt for example, there is a shuttle from Waterton to the Border Crossing with "
www.hikewaterton.com" but only runs once a day. So i called them and for higher fee, one could arrange a private shuttle. Am just suggesting that these are things you might want to have checked into so that when you get to the Permit Desk, you have the most options for a great itinerary.
I know there are alot of variables involved with a WalkUp but i hope this is helpful.
Best Of LUCK!! Tam