Alright, here's some pics. The hose shop I went to was actually an air compressor shop, so I hope that helps people in the future. I'm holding the fittings backwards in the picture, so it's hard to see, but the bottom part of the fittings are actually the fittings in the red box (pictured below) cut off the old hardlines, and merged with the push fit fittings. They are then pushed into the hose and hold surprisingly tight. After that, they can be screwed into the lines going to the rear of the car like they would normally.
Here's the side that goes into the rack. They had the exact fittings with O rings at the shop and put push-fit fittings on the other side.
If you're replacing the lines in the 4ws rack in the back, I'm sure its a very similar process
edit: Just a note, if you use push-lock fittings they will pop off on your first hard turn. One hose clamp keeps them on but I put on two very tight just to make sure. I recommend avoiding push-lock if you can, just make some an lines or something