I think every single S&S bike will have to be packed differently because each bike will have slightly different dimensions for the different parts. My bike has 26 inch wheels, I can leave the tires on the rims but I usually use 57mm wide tires that need to be deflated to fit everything into the case. I do not have a cassette, have a Rohloff internally geared hub. When I have packed my folding bike in that case, it uses a cassette, I remove the cassette but I have no idea if you would need to or not.
I assume you have the S&S Backpack case from your description. I have that case. There is no center support. I made one out of a couple pieces of very thin plywood (maybe 1/8") and a couple dowels and some screws. Not sure if it is needed or not, but I feel it is safer to have that. I also cut a couple pieces of Coroplast (bought a 4X8 ft sheet at Home Despot) at 26 X 26 with rounded corners so that my case sides are stiffer.
The fenders will not fit in my case, and the rear rack won't either. When I have flown with a bike, I needed to check two bags because of my camping gear too, so packing the rack in the other bag is not a problem for me. My S&S bike is quite heavy duty, thus is heavy, I need the luggage scale to make sure I have removed enough stuff from the case to make it 49 pounds, usually pack my pedals and saddle in my other checked bag.
The second time I packed my S&S bike, I made a critical error in my first several attempts and could not get it to fit in the case. Fortunately this was the day before my flight home and I had the spare time. I figured out what I did wrong and packed it right. When I got home, I took lots of photos as I unpacked it so that next time I packed it I could get every bit in the correct order of packing, in the correct orientation. After my third trip I was happier with my packing, took replacement photos.
Headset parts can be numerous and have to be in the correct order, and orientation. So, when I remove the fork, I put the headset parts in order on the steerer tube for storage, use a rubber band over the end to keep them in order. That gets another photo in case I screw up, so I can refer to the photo.
I started out using double sided velcro strips to try to tie most of the big parts together so that the frame members and wheels could be lifted out of the case for an inspection by TSA. (And I included a note to TSA stating that.) But over time I am slowly switching to using zip ties instead. Carry a tiny little side cutter for removing zip ties. Toe nail cutter will also work.
I have a thick walled piece of plastic tubing cut to 135mm. I put that in the rear dropout to make sure that the frame is not bent if the airline stacks a ton of stuff on top of my case. I use bolt on skewers when I travel, not quick release. Skewers use a 5mm allen wrench. Use that rear skewer with that plastic tube to reinforce my rear frame piece.
I have read many people say they can pack or reassemble bike in less than an hour. It usually takes me about an hour and a half. Almost total disassembly, but bottom bracket stays installed. Even all three water bottle cages have to come off.
Loose bits usually go into a ziplock or padded bag. In case you lose some screws or washers, bring spares. I always have packed and unpacked outside.
Everything packed, below:
I cut some rubber sleeves from an old inner tube to put over the ends of my S&S nuts to keep the threads clean. I do not carry the S&S grease on a trip, that is one reason I use the rubber sleeves, to keep things clean, then I do not need to add grease every time. You can see the rubber sleeves in photo below:
I considered trying to cut my rear fender into two pieces that I could then attach together again Rinko style, but eventually decided against it. Instead I use a couple tiny little plastic fenders I bought on line from asia (before tariffs) that provide a tiny bit of coverage.
I remove the crank arms (square taper). I use the XLC crank arm tool because it works with a 15mm pedal wrench and an 8mm allen wrench. My S&S wrench includes both a 15mm open end pedal wrench and a 8mm socket, I cut a piece of 8mm allen wrench from another wrench (tool steel, I needed to use a Dremel cut off wheel) so that I can insert that 8mm stub into my S&S wrench. I assume you are not so lucky, my bike manufacturer made their own S&S wrenches, the 8mm socket was for emergency use on a Rohloff EX box to shift gears if a cable broke. My primary tools for travel are below:
I carry a lot of other tools too, assembling and disassembling a bike is much more time efficient if you have better tools than just a multi-tool. But if I needed to, I could do everything with the above.
I tried self extracting crank arm bolts, but the self extracting mechanism on one crank arm self extracted itself somewhere in the middle of Iceland (below), and to pack my bike I had to remove the self extractor from the other crank arm, and of course I did not have the tools for that. It was then that I decided in the future, bring a real crank arm tool.
I suggest you always carry a tool that will tighten the couplers. I have had this bike for 12 years, only once during a ride did a coupler come loose on me, but after stopping to hand tighten the coupler every couple miles on the way home I now carry a wrench with me with my spare tube. It is a cheap wrench that is adequate for the task, not a genuine S&S wrench.
My last trip with that bike was a five week trip in the Canadian Maritimes. I wear my helmet onto the plane, put it in an overhead. I do not want baggage handlers to break it. My luggage for that trip is below:
I managed to recover my costs for the couplers and the S&S Backpack case before some of the airlines dropped their oversize fees. Be even though it now is free to fly with an oversize bike on the airline I usually use, I plan to continue to use the S&S case in the future as it makes getting my gear to and from home and airport, or a hostel and airport in a foreign country so much easier.
Storing my S&S case, I remove the side panels, but with the corroplast sheets in it I do not fold it. But I could fold it if I had too. Was easy to store in a luggage room at a hostel with some of my other stuff also in it. In the photo below, was only about 2 or 3 inches thick with the side panels removed, so the hostel staff did not mind storing it for me.
Those are the items that come to mind. I am sure you will have questions.