The later is closer to how most professional game dev competitions I've judged for are run (PAX10, IndieCade, Game Dev Choice Awards, etc...). The judges all split up the games and then come back to discuss what they liked and to recommend games for various awards. The judges will often then play the suggested games in a second round, but at least every game is guaranteed a fair shot.

Not having any judges play some of the games perpetuates unfair disadvantages that already exist in the ratings. For example, one of the games in this jam is made to be played by people who are blind and intentionally features a blank screen in hard mode. That will likely hurt their rating for "visuals" and could place it further down in the overall ratings. That should not disqualify it from recognition in other areas.

(The best audio in the world could be featured in a crap game, their audio person should still get an award for best audio.)

Additionally, for games with fewer ratings, 1 or 2 people can tank the ratings for what should be a 5-star game. If someone made a game featuring a transgendered character, a couple of transphobic people could intentionally tank the game's ratings out of spite. The number of ratings a game receives is already influenced by things like popularity on YT/Twitch, whether you worked on a team, and whether there is a cute/attractive face on your title card art.

I think if you reach out to your judges about this now, you'll find some of them are likely to agree to split up and play the games that weren't already "selected".