I have set up a match with another school chess club that has players from 4th-6th grade.  The other chess club coach and myself are complete novices in setting up a match like this, so I was looking for help/advice. Here are my thoughts, and I wanted to get some feedback on problems with this, or what other methods might work better:

we have about one hour to do the match, and I would really like the kids to have a chance to play two matches each. Each of our chess clubs have about 20 kids, and I would say about 80% to 90% of them are able to finish a match within 30 minutes. My thought is to group the players into groups of four (for example, top two players in each chess club) and play round-robin for two chess matches. Regarding fitting a game in in 30 minutes, the kids are not used to using clocks so that doesn't seem a good option. The only thing I can think of is, whoever has captured the most material (unless there is an imminent checkmate on the board) is declared the winner. Does someone have a better option than that? Also, I'm sure that there will be an unequal number of chess players, so what happens if one team has 19 players and the other has 25 players? Any novel ways to handle that?

You have one match each, and only one match each, in a match. 

You force the kids to use clocks - its not hard. Your idea of capturing more material is absurd - material count often means nothing.

You set a reasonable limit to the number of players per team, usually five. Make an internal competition to see who those five are if you want.

If I am a bright kid and I know your rules I will win a piece early and then stop moving until the time expires.

It sounds as though you really shouldn't be doing this until you have a little more experience.

Maybe select your best ten guys, toss a coin for who has white on board one, and alternate black and white down the other boards, and use clocks, the game is impossible without them. Also there is nothing more enjoyable than making a killer mpve, slamming the piece down, and slamming the clock. If you do not have clocks, someone will be adjudicating drawish games, you do not want to go there. 

If your kids have not done this before, they need to understand a couple of rules,

No wandering about making a noise and no talking about their game to others.

It is much better to be polite, and shake hands and just be a nice guy.

One way to encourage this is plenty of snacks and drinks, your guys will sit and eat cookies for ever, lends a nice atmosphere to the game room.