"So my suggestion is, leave the 100 mine limit per sector in place, but make the minesweeper component be destroyed in the process of detonating the mines. Not the minesweeping ship itself, just the sweeper component"
An interesting idea, not sure if I am totally sold on it but it does sound promising. I too believe that mines are massively powerful at first, then (like drones and fighters) become almost useless mid-late game (and med/large mines are just useless in themselves).
I just have one 'part' idea to add to your own. How about the Minesweeper component having a 'damage capacity' that goes up with level. ie, level 1 sweepers can destroy 'X'damage amount of mines and level 2 can 'soak' that plus a little more before they become a 'destroyed component'. I guess this would make the sweeper some sort of 'armor' that only mines hit first and that doesn't count toward ship strength at all. That and leave it moddable of course so we can make 'budget' minesweepers etc (or use Mounts to differ the damage etc..

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That and it is my firm belief that level 1 minesweepers should be 20kt not 30kt in size. Just like shields level 1 is 30kt and then goes up to 40.