In terms of the SoH and Tumble checks, an Item Familiar is boss. You need a 35 Tumble check and a 40 SoH to auto-succeed.
Longstride Shifter Druidic Avenger 5/Factotum 8/Horizon Walker 1/Ardent 1 with Dark (+1LA) and Shadow (+2LA) templates and the Quick trait.
32PB: 18 Dex (16 pts), 18 Int (16 pts), becomes 20 Dex, 19 Int with racial adjustments and stat bumps.
Feats -- Longstride Elite, Item Familiar, Cheetah's Speed, Wild Talent, Speed of Thought, Fleet of Foot, Endurance, Craft Wondrous Item, Run (2 flaws, 1 feat bought & retrained)
For the relevant skills, we have:
Tumble +17 ranks +8 Dex +7 Int +2 Jump synergy +1 Item Familiar = +35 total
Sleight of Hand +17 ranks +8 Dex +7 Int +2 Bluff synergy +17 Item Familiar = +51 total
UMD +17 ranks +17 Item Familiar -1 Cha = +33 total
Horizon Walker lets you be immune to fatigue, so you can keep walking and not sleep (though you need to sleep to regen spells and use/day things). Carrying capacity = haversack.
WBL (level 15) = 200k
Items:
~Otyugh Hole or similar (3000)
~Haversack (2000)
~Boots of Running [continuous Haste and Footsteps of the Divine (Farlanghan), factotum only, must have Run feat] (5*3*2000*1.75*.9*.7 = 33,075)
~Gloves of Dex +6 (36000)
~Headband of Int +6 (36000)
~Periapt of Wis +6 (36000) [for Ardent, Druid]
Remaining gp: 53,925
Speed:
Cheetah's Speed 50
Longstride Shifter +10
Longstride Elite +10
Dark Creature +10
Quick trait +10
Fleet of Foot +10
Speed of Thought +10
Freedom Mantle +10
Haste +30
Footsteps of the Divine +50
Shadow Creature *1.5
= 350
You can also get extra standard actions to move some more by spending Inspiration points as normal. If you're willing to remove a few of the feats (like taking out Speed of Thought and Wild Talent) you can get Font of Inspiration to do this more often.
EDIT: Oops. I can is maths good. 200 * 1.5 = 300, not 350.