Personally, if the planets are so heavily mined, and the player likes to build more mines during his turn, its near hopless. So, I simply blow up the systems Star, and be done with it. Then move in a planet maker and rebuild the star and planets. Colonize, and move onto the next system.
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"We've made too many compromises already, too many retreats! They invade our space and we fall back -- they assimilate entire worlds and we fall back! Not again! The line must be drawn here -- this far, no further! And I will make them pay for what they've done!" -- Patric Stewart as Captain Picard
UCP/TCO Ship Yards