imho, mines should be able to be shot down by anything with a gun. Not so hard to hit a immobile ball of steel when you can take down speedy fighters.
It waste some time to destroy all the mines, but time is important in this game...
a minesweeper ship would be a waste, little use outside of just that.. minesweeping. Not very fun.
Just make the mines a valid target for any ship would work i guess. Mines are and were always more about controlling the movements of the ennemy and wasting his time and ressources. They are not winning wars.
or make the mine vanish after a while, limited lifespan and LONG cooldown for the ability. so it a temporary measure that CAN be countered anyway.
just the 2 cents from a guy who dont have entrenchment.