If your going to cut through then start at the back, cut the plastic-y bits out, see if you need to box/frame around the metal so it doesn't let go across the whole width of the seat. DON'T cut out the shape in the foam/fabric layers. Keep them whole and pull/stretch/wrap them into the port and try join them to the backing to make a nice factory finish.
This is super generic advise, measure a bazillion times, cut once (especially as you only have one seat! hahah)
I think your after auto upholstery advice not box building, stick up a well lit shot of the layers in your seat so the materials are obvious. With the box is this hole in the seat going to add to the port? Factor that in. You may need to trim some off the inside lip, the box volume will be far less critical than the port volume.
