IIRC, the usable Extract waypoint area there is actually rather large; you often get the completion for that objective before all your Mechs are even in the last 'room' with the marker. Perhaps the last 'Mech alive was close enough to trip the objective, and dying didn't cancel it out.
Go closer to the outside edge of the north and east sides. Except for an obvious super-dense patch up near the NE corner(I used to love dragging the Shootists over there with my scout 'Mech and trick them into killing themselves), it's completely free of mines.
There are also some extra RPs to be found in that mission. There's one obvious resource building on the island just north of your starting position, guarded by a pair of Drillsons. There's a lone RP vehicle northwest of your starting position(covered by a couple of Centipedes), and another in the damaged "middle" Steiner base, just across the river from the Davion base. The two RP vehicles together will let you call in another Repair Truck, without cutting into potential 'Mech salvage RPs.