Paravane sweep gear rally only works against moored mines, which only occur in water shallow enough to anchor those mines. Carriers were just too valuable to take into shoal waters, adn if that were necessary, smaller, more expendable minesweepers could be sent on ahead.
The rigging at the bow is a combination inhaul and outhaul. The sweep cable is laid out, outboard of all lifelines and ship's structure. This is tied off with marline and small stuff. The paravane, otters, and the like are rigged at the aft end. The inhaul is brought to deck level, and the forward (inboard) end of the sweep wire (or wires) is made up to a shackle on the un/out haul/
The paravane (or paravanes) are let go and the towing eye is hauled down to the forefoot. The 'vanes then stream the sweep wires out.
For ships without a fixed foot at the bow, there was a sliding foot, which was hauled down into place with yet another pair of chain hauls.
Which makes for a bunch of test questions to grill midshipmen in NROTC classes, and to complicate the 1c & Chief's Bosun's testing materials.