I've never trained or dove side mount but that thought has crossed my mind - if I was sure to drown because of an empty tank but yet carrying a partial tank with a bad first or second stage on it - I'd attempt changing first stage regulators out while holding my breath (blowing bubbles) - better yet, with a buddy, share air while switching.
Why not try it?
On the dive that moved me to isolated manifolds, I came very close to doing an in water regulator exchange.
The particular issue I had, using cyklons, I could have unscrewed the diaphragm section and exchanged it - had i been certain that was actually the issue.
That meant one of three choices,
1. Remove the problem diaphragm assembly from the problem regulator. Remove the section from the working primary regulator. Reassemble.
I figured that was a bad idea, i.e. go from having a working regulator, to potentially having none.
2. Remove the problem diaphragm assembly, and exchange it with the decompression gas diaphragm assembly. That would compromise the decompression phase of the dive. [1]
3. Disassemble the diaphragm section of the second stage on the bottom clean and reassemble. That would have increased the decompression penalty, moving us out side of the runtime plan, potentially outside the KYAGB plan [2].
That assumes, I had actually identified the fault correctly. One advantage of sidemount is it is a lot easier to swap a complete regulator assembly. Other than you are potentially compromising a working cylinder, as well as the problem cylinder.
I regular strip and rebuild Cyklon second stages, however, I have never attempted to do this 'in water'. I have dropped pieces in the workshop, which is a pain, dropping a component 45m underwater is a little more concerning!
[1] I know that a big section of the caving community like Cyklons. A lot do not refit the circle that retains the diaphragm front section. This allows them to remove the from of the regulator quickly to clean out the diaphragm if its been compromised by grit and rubbish crawling through a tight section.
[2] KYAGB - Kiss Your Ass Good Bye