Over all I absolutely love the idea!! It's one of the mini-games, Minebulas, we play during the VIP lobbies if we can't get enough player to run a full VIP lobby or if we want general silliness. We only use mobulas with all 5 gun slots mines because we thought running with squids took too long to get mine kills and we do Squid Derby if we want general silliness with squids.
Caution: Watch out for those unintended capturing of the points. They ruin games like this.
My only slight concern, keeping aware that score is secondary, is the no ref part with captains calling out their kills. I don't see an issue as far as trust or anything like that but simply from watching this as a ref in the VIP lobbies, the kill feed can move kills rapidly off the feed and sometimes a captain may not see if it's their ship that made the kill or not...especially if you have multiple ships in one area with possible 5 mine launchers per ship x 4/6 ships x 5 mines per mine launcher that's a lot of mines. Without watching the kill feed I see that this could become a point of tension, regardless of how fun players intend this to be someone gets competitive when scores get close. Not to mention captains having to remember if that was kill number 4 or kill number 5, etc.
So my only suggestion is think about having 1 ref in lobby. That's something, Anakin, you personally can do seeing as it looks like you are aiming for 1 lobby. A simple list of all 4 to 6 ships and a tally system each time they call out their kill but keeping in mine you are watching in case captains couldn't watch the feed fast enough due to watching arcs or watch the approaching mine field.
Also just curious if you are intending to have a time limit?