The KYDD upright electric basses use something similar - but it' s opposite at the same time:
They use a bridge tuner that is very similar to what you are thinking - and at the nut end, a good old fashioned locking nut - hence any kind of strings can be used on their 34" scale model
I am a huge fan of these instruments, huge fan.... it's a very brilliant but at the same time simple design.
Of course you do not get the height adjustment - on the other hand, I would think running a "zero" fret between the mute and the locking nut would solve any height issue.
Of course, I could be wrong on that....
Food for thought if nothing else.
I like hearing when people are thinking of designing things.
*unrelated - but I spent all morning trying to figure out how to make a strap system which would enable a Stick player to play sitting down - where the strap goes through the belt clip.
I am very close with a very pratical cheap solution on that............
Big George W
East Derby CT
WARR, Mobius Megatar , Syme, KYDD, Ovation , Steinberger , Tune, Schecter, Musicmakers [lots !!], Ironwood Stick 
digitech, T.C. Electronics, ART, Lexicon, GK, Markbass, EA, Bag End, Guild/Hartke, SWR, EV, Radial, Furman
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