I use the Axian storage boxes, first when I took every car off the layout several years ago when the floors were being re-done, second as I move inter-state where I have a lot of car storage boxes stacked in my other house. In the first instance, where some cars stayed in the boxes for a year or more, the only models I had any real problem with were the Branchline. Any cars that weren't weathered or Dullcoated stuck to the foam to the extent that I ripped the doors off of quite a few boxcars on one or both sides, and sometimes the car stuck to the top side foam strongly enough to hold it.
I know from working with the Branchline paint that it sometimes stays slightly tacky even after a number of years. So my solution is to use sheet foam intended for packing dishes, which I lay into the bottom of the box and then lay over the cars, in any box that has Branchline cars. For my purposes, that's good enough, since when these cars get unpacked, I'll go through a program of replacing the original coupler pockets with Kadee 262 anyway, along with painting wheel faces and anything else that I didn't do when I was originally building all these the first time, including a few more reweighs.
On a related note, the replacing of the draft gear involves drilling a new hole, tapped 2-56, between the existing two mounting holes for the OEM coupler pocket. I've found a sweet spot for this hole, just far enough outboard of the inner original mounting hole to clear it by about 1/16". This is far enough toward the end of the car to avoid biting into that mounting hole, and far enough forward to avoid hitting the steel nut weights that came with the kits. As a compulsive OCD kit assembler, I always tried to position that nut so that a flat was toward the end of the car, which helps now in the modification.
You can determine this position by eye by laying the 262 draft gear against the floor of the car, with the reinforcement around the draft gear opening flush against the car end, and marking the center with a couple of turns of a small drill bit. Once you've done that, you can verify that the hole is centered transverse to the car centerline and in the right position with respect to the existing holes before final drilling.