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Just in case, I'd like to point out that you're not quite discussing the real problem. On one hand, you're exaggerating its scale, and on the other, you're downplaying the real consequences.
Even if a tournament doesn't have an Overtime (OH) rule, two players who want to play with OH will play with it.
Even if a tournament does have an OH rule, two players who don't want OH (either because they rush the timer or have some other personal preference) will agree to play without it. Furthermore, in this case, some players simply won't play because (for various reasons) they can't afford it (since Zhenya is surprised, I'll just say it plainly – there will be such people). But this loss is unlikely to be significant in the long run.
The problem only arises when a player who wants to play with OH meets a player who wants to play without OH.
Considering that this doesn't happen in every game, I'm not sure why people are being so inflexible and refusing to sign up for tournaments. But I won't criticize them for it. Playing against noobs is boring anyway, and if it also takes up extra time, it's doubly boring.
Here, I wanted to point out that a relatively small number of games are being discussed. And the decision is about prioritizing one over the other. I believe that an open vote is the ideal way to make this decision. But not to decide the issue by a majority vote. Rather, to see how people will behave when making one of two decisions. The answer options could be something like: "at the moment" 1) I'm only willing to play with OH, 2) I prefer to play with OH, 3) I prefer to play without OH, 4) I'm only willing to play without OH, 5) I don't care either way. It's a vote in form, but in reality, it's a survey of opinions.
And the most important thing to understand before making a decision is what percentage of participants the tournament will lose in one case and what percentage in the other (answers 1 and 4) – so that the organizer can make a decision knowing the consequences. Answers 2 and 3 will be useful to decide at what stage of the tournament OH will be in effect, if you're thinking about a different approach at different stages (for example, I think that OH shouldn't be used in the more massive early stages, but in the later stages, where only the top players remain, the conditions can be made stricter – like, you came to the tournament to test yourself, to prove that you're very good – prove it with OH).