Under the current system, a single player can deploy an unreasonable number of mines in a sector that has a station or a HAC. The player deploys the mines, docks and reloads, and then deploys more mines, etc...
Killing the player has no effect on the mines, if the player is homed in the same sector.

If the player leaves the sector, the mines all cease to exist. This aspect has been generally acceptable, and if docking had the same effect, it would mitigate a majority of this problem.

Could this solution (or some other effective solution) be quickly deployed, as I expect this to be a continuing (and potentially increasing) problem.

(and while your at it, consider having this effect all ordanance, so that missles, energy, and flares, also cease to exist on docking.)

Second. Except for the rocket/missile/energy bit.

I'd prefer that there were some sort of dedicated station turret or defense for knocking out mines around stations. I kinda like a minefield around a HAC.

Minefields are awesome.

Mines can be shot down, right?

Yep, they also time out in 10 minutes, meaning that maintaining a minefield is a constant work.
I don't think there's any pressing need to adjust mines right now.

Yeah, shelve this idea for now, and we can pull it out of retirement when it actually becomes an issue. Until then, mine mechanics are fine as they are.

I don't think the L-mine deployment is a problem atm. Particularly for HACs: it makes sense for HAC defenders to deploy passive defenses. The mines timeout anyway.