You just need to be absolutely sure that someone who doesn't really care at all about putting the case back together properly can do so with minimum time and effort involved. It has to be easier/faster to put it back together properly than to put it back together incorrectly. Whatever is the fastest/easiest way to put stuff back in the case, and get the damn thing closed back up is what TSA will do. They have absolutely no incentive to care what happens once the thing that isn't a bomb leaves their hands.
This is why zippers are great, up until they get broken. It's either zipped, or it's not. Pretty hard to f**k that up through not giving a damn/expediency.
Definitely don't tape/cling wrap the thing together. TSA will cut the tape off, and then *maybe* tape it back together. Maybe. Definitely not with the same level of care you did. Definitely not at all if their are even vestigial straps that they can kinda get to hold the thing together long enough to get it back to the airline, at which point it isn't their problem anymore. Or the airlines. At that point, it's no one's problem but yours, and you're SOL.
Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
Coaching and bike fit -
http://source-e.net/ Cyclocross blog -
https://crosssports.net/ BJJ instruction -
https://ballardbjj.com/