Hedgewars seems like a fun and easy one to set up. It's free and open source so modding is far simpler.
Pic related: normally CPU teams can't have flags, but we can delete the code that enforces it and recompile!
Cosmetic customization examples
As you can see in the picture, a hat is overlayed over the character. It can cover the whole player. I can make the base player invisible if people wanted to do full body mods (I would choose to keep arms and legs) but it's easier to just not do that.
Flag at the bottom.
A marker placed when a player on your team dies on land.
Alliance colors chosen at start of match.
In-game reactions and banter from your team.
If we use a randomly-generated map, this controls stuff like background music and textures.
Functional customization examples
Maps to play on.
<However we can make more customizations ourselves
We can let teams choose a modifier active in their games. e.g. /lego/ has unlimited girders, /fascist/ has each team start in a section of the map instead of randomly scattered, /otter/ could have an early or faster sudden-death water rising
Normally there are 5 bot levels, but we can probably add one for each team. We could use this to make each team's AI forget how to use the weapons, then have teams pick 8 (for example) weapons that their AI knows how to use.