OOH!

I would leave the vibrato on the guitar because it looks really nice.
A couple of seconds with an arc welder would solve the tuning problems.

Oh, I'd leave it on for looks, but add a VibroStop for stability. Those sideways ones are crap for functionality, so I would just replace the mechanism with the big block of metal.

MojoAxe VibroStop Sideways Vibrola Conversion Kit for 1960,1961,1962 Gibson SG | eBay

VibroStop.jpg
 
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