I would suggest implementing both a "soft" and a "hard" wall to entering an election - analogously how the site both implements ("soft") text which warns new users about the quality standards of the community and ("hard") automatic question/answer bans.
To start with "soft", I think having a "pre-nomination" or "standard-setting" stage to each election would help - this would probably take form similar to a meta post. This ought to include both the tangible and intangible qualities that the community is hoping to find in a moderator. What sort of badges the community likes to see, how active they expect moderators to be (and doing what), etc. would likely fall into this category. The resultant page of this discussion would be displayed to anyone who wishes to nominate themselves. (And perhaps some soft-checks on reputation can occur too - e.g. additional warnings for anyone with particularly low rep)
Personally, I would not have nominated myself (and later withdrew) if the meta discussions that occurred after the nomination page opened had instead occurred before - though at least, for next election, any conscientious but naive person might find the posts resulting from the current election by searching meta - and might, at least, eliminate however much of the current nominations are in good faith but poor judgement.
To supplement this, it would be good to have some hard requirements. The bar, I think, for these should be set to the level of:
The community trusts you to consider your own merits carefully before nominating yourself and has no objective reason to disqualify you from moderation.
rather than the higher level of
The community believes you may posses the qualities to moderate.
Now, take this with a grain of salt (because I can't hope to have much idea of what you all want here), but I would suggest this hard check run on the magnitude of:
- User should have 3,000+ reputation (for experience with close votes, at least)
- User should have 100+ reviews in some queue.
- User should have posted & voted on meta (with positive score).
- User should have raised several helpful flags.
and perhaps "User has at least $n$ of the badges: " - exactly what these requirements would be a separate discussion.
I think that, in conjunction with the soft wall, this would be very effective at not disqualifying plausible candidates, but cutting down on extraneous nominations - since there would be more than a big shiny "nominate yourself" button between a user and nominating, and since anyone with access to that button would (hopefully) have integrated enough into the community to think critically about whether they ought to press it.