A trem setter on a trem equipped guitar solves all of those problems pretty quickly. The trem setter will get you through the rest of a song on a broken string guitar the same as you would on a fixed guitar. After that, you either have to fix the broken string or switch guitars......... no difference between the two types.
In all the live playing I have never tried the trem setter. If it works as well as you say it does then I will give it a shot next week (if I get one).
I guess the more I play the more utilitarian I get and it's like a job where I want to do it with as few issues as possible. I remember trying to bring a stereo setup I had, when I first started, and I had every pedal on full without regard for how it sounded. I thought the faster I played and the more gear I had the better, and it worked through small gigs.
When I got my first big gig at 18, the professional sound man came in and set us straight. It was San Diego Civic and the speakers, dozens of them and lights were up on rafters that literally looked like a UFO above us. He put 57s (Shure SM-57) right in front of one amp which was barely turned up and let the thousands of watts in his PA do all the heavy lifting. I went in dry with no reverb and he supplied that effect from his board.
As a kid I thought about all the gear I used to see up on stage with the likes of KISS then I found out from him, who did all these bands who came by that stadium, that he put a single 57 or two on a working Marshall and told me the rest were either turned off and that most of the huge Marshall cabinets they used as a stage were mock ups.
But being a kid I thought I was right and there was no way a 57 could go through a small amp and fill a whole stadium and get a big sound. Why would KISS or AC/DC use fake Marshall cabinets? Well he was right.
Come to think of it, if a 58 mic could take a voice and fill even bigger stadiums like Hammersmith or Budokan, then why not a mic on an amp? He was of the belief that keeping it simple was the most important thing all on things from guitars/basses, to pedals, to amps. Sure you could go wild with trem and try to be Eddie Van Halen, have a ton of distortion and reverb on, dime up lots of effects, but what sounds "cool" in the living room won't sound the same way at the Cow Palace or San Diego Civic.
I translated the simple philosophy to much smaller gigs and the less is more philosophy and trusting your fingers, a single mic, and using the PA as a simple formula will win more times than not.
Now if I had a guitar tech standing in the wings with identical Floyded guitars with every push pull and flip switch on the guitar (like the mad projects I like), then I wouldn't mind. But there's almost no feeling more defeating than having a guitar with too much that can go wrong then actually go wrong when you play live. I notice many established bands who literally switch out their completely stable Floyded out guitar at every song. There's a reason big name bands have their guitarists travel with a dozen guitars each during live concerts, and not wanting to slow down the flow due to technical issues is a big reason why.
Heck there are a ton of guitarists right here who admit they have never played a live gig who have arsenals bigger than many rock stars.