I think the official way to address that would be to have runoff elections, narrowing the field of the second round of voting to a small enough number of candidates that you could reasonably try most/all of them. e.g. re-run the vote with the top 10 candidates as finalists.
I think many people would participate in the second round and not the first, and that they’d find time to play at least five of the top ten, which is at least a representative sample.
Having said that, you can simulate this for yourself just by observing the reviews for games while the contest is running. After a couple of weeks, a few games will have a larger number of reviews, and if you look at the scores in those reviews, you can identify some front-runners. Then, try a few of those.
Once you’ve played a few possible front-runners, you can probably assume that any other game you try can be fairly compared against them, allowing you to more confidently rate a game from 1 to 10.
That’s the way I normally handle this for the SF Bay Area IF Meetup. During IFComp, but before IFComp is finished, I look for games with a large number of reviews and games that seem to have high averages. (A spreadsheet normally forms, which helps considerably.) Then I suggest those games at the meetup.