Skip to 3:54 for the successful attempt.
Using the Napsack, I am able to get on top of the stump next to the Glutton's Kitchen. This allows me to skip two barriers: The one in the water blocking the Submerged Castle and Massage Girdle, and the electric fence in front of the Glutton's Kitchen. Utilizing this glitch (and MilesSMB's scale glitch), I was able to beat the Perplexing Pool in one day with only 45 Pikmin. Day 5 (Perplexing Pool) of the 7 day 45 Pikmin run is here: https://www.youtube.com/watch?v=82ZWoamPS-0
My best advice for pulling this off: you want to be pretty close to the corner, but not quite in it. This way, the Pikmin carrying you will hop over the ledge sticking out of the stump, since it's in the way of their trip back to the Onion. Dismount as early as you can, once the Pikmin carries you, to land on top of that ledge.