Climbing approach to Ice Cube Canyon (the Maze)?

Are there any good routes (<= 5.9) that can be used as an approach to The Maze canyon?

I'm looking to go through the Maze, but it would be great to replace the approach hike with some climbing.  The sneak route for the canyon seems to do a good job replacing the approach with some scrambling, but I was wondering if there were any actual climbing routes that can be used to maximize the fun.

The most epic thing to do is climb through the maze in reverse, starting with the first pitch of burlesque. This brings you to ‘the sanctuary’ which will be the start of your adventure. Beta for this can be found in the comments of ‘beta blocker corner’. To get from here to the NE arete of bridge mountain is a fun challenge, no fun if I give you all the beta though.
Another option is to climb something like birdland (traverse up and right after p6) or super s, and continue to the top of bridge, then drop into maze.
last obvious option would be to research the 52 peak club beta for holiday peak. There is a 5.9 bolted arete that gets you from there to bridge connection. Hike from bridge connection to base of NE arete. Summit from there then descend to start of maze.
enjoy. 

I have parked at Icebox, taking Dale's Trail around into Pine Creek, scrambling up the north fork (underneath the Pisces Wall) and on up to the Bridge Mt-Bridge Point saddle. From there skirted around Bridge Mt and soloed up the NE Arete of Bridge. Reversed the Bridge Mt hiker's route to the limestone, dropped into the very top of the Maze (we did the full version of the Ice Cube) and took it all the way down and back out Icebox Canyon again. This was a fun day.

We did it in July on a 100° day and with wool long underwear and fleece jackets - but no wetsuits - ended up nearly hypothermic after several of the swims. I would consider a winter or early spring attempt to be a serious undertaking… Thick wetsuits/drysuits being mandatory… Ice would change everything.

Ideally you’ll have plenty of water but not stagnant water. I would save it for just after a summer monsoon storm which would hopefully flush all the ick out.

If you are a decent climber you can expect to cut the rappel count in half, plus or minus, with skillful down-climbing. BluuGnome mentions 23 but I think we did 10-12.

Also, I noted that the only rappel you need two ropes for is the final one, and I remember seeing natural pro opportunities about halfway down. I think if I did it again I’d bring a couple bail pieces or possibly an Escaper instead of a second rope…