I wanna approach mines with a little Cybermen logic. The simple solution is to "DELETE!" them. As you say, space is big. It should be nigh impossible to manage to get hit by a mine.
If we, on the other hand, want to keep mines, we can always "UPGRADE!"them. We can't simply add powerful trusters, that'd turn them into missiles. But what if we stop looking at mines as munition, and turn them into small drones? Say... 5 dtons or something. Give them low or no maneouvreability, a sensor package and fire control. When anything comes close enough, they launch their payload, which could be a one-shot missile barbette or a single torpedo, for instance.
There could also be an option fo fire them remotely, based on sensor data from a nearby ship. Perhaps a cheaper mine option, that can't fire on its own at all?
We could also go nuts and create a mine-laying module for cutters, allowing them to carry and deploy 4-6 mines, plus a control room to supervise and remote-control them. Said module could also be used to pick up spent mines, re-arm and fix them.
Obviously, the idea needs more thought and polish, but it could work. Perhaps?