Well, you "can" use classical snowboard hardboots in your split,but there might be some issues with the ramp angle.
Some people i know have used Kofflach and Asolo high mountain climbing boots in their snowboards on high ascent/descents. Gives warmth and climbability, but lacks support in upper cuff. That you can get by with some customisation (well,maybe some booster straps and higher and thicker liners?).Some of those have complained a bit off the lack of support on the toeward edge on hard snow,if they havent modded the boot.
I even have once seen a guy that rode a split with garmont megarides, a randoboot...
Dont know if he was riding with the walk latch on or what.
Hmm, i could be tempted to test that some day... 
The biggest difference i think would be the catching the edges since you are much more rigid on the board and cant even out the small núances that you do with the soft boots.Especially the transfer from back edge to toe edge could be the most tricky part....Brr..the tought itself is giving me shivers...
Why do you need stiff booties? Ankle problems or are you just tired of messing up with lace-up crampons and loosing the in some couloir?
The floggings will continue until morale improves.
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