Fixing it is actually really easy, they just have to stop reviewing the call made, and just review the play as if no call has been made. All they need to look for is proof that an out should be called and in the absence of that, the review should call the play safe.
Whatever language they want to use... clear and convincing, beyond a reasonable doubt... etc is all semantics that everyone will interpret differently anyways. It's incredibly easy to sync up EVERY camera angle on any play in the digital age and run them frame by frame in a matter of seconds.
THEN, the replay room should be required to log the entire process and explain why they made the call they did and that information should be accessible to all teams the following day for transparency, as well as MLB so they can review the calls to make sure they can intervene going forward to make clarifications.
Like, in the case of Varsho's catch... the review team would have to explain why they ruled it a non-catch, in detail. Not just "well, we saw go in the glove on the fly, but... there was this one frame where we think it might have fallen out and we're not sure so...we went with safe"... that wouldn't fly.