re box dimensions, cardboard boxes sourced at bike stores can vary in sizes depending on frame size bike they receive. One of my last ones I used was 148x19.5x82 and was a reasonably easy fit for the medium troll, with rear wheel, rear rack and rear fender still left on, front wheel and front rack off obviously, and seat post pushed all the way down and seat was still a bit below top of box.
I tend to put my sleeping bag or tent upnear front fork, which always has good sturdy plastic piece in dropouts, taped on and some added foam taped under as well for shock absorption.
Ive also used slightly smaller boxes in the past, which were a bit of a pain to get bike into, but specifically wrote down these dimensions, from a box from a bike store in Mexico, and worked fairly well fitting in wise.
Ive never had them actually apply and measure for the "official" dimensions limit of X+Y+Z, could it happen? I dont know, but as I have always arrived with a clearly official bike box with bike brand logos on the side, and they are accustomed to seeing bike boxes, its never happened to me so far (touch wood).
Ive only flown Canada to France, to the states, and to a few places in Latin America, with (overall) bike friendly ish airlines with reasonable rates for bike boxes--as long as you respect the weight limits, which I have always been under or just a bit close to limit, but always under.
Any other airline than JAL would be fine. Their baggage allowance is two pieces at 23kg, which is unusual for outside of the USA (or flights to the USA) but they are ruthless with the tape measure because rules are rules in Japan, unless they aren't (but mostly are), and I've had our boxes measured by them ,even though they were clearly oversized luggage so why bother! Anyway, it'll be entertaining getting my bike with the Rohloff and ATS speed drive in there. The derailleur bike will be fine, it has self extracting cranks but the ATS cranks are hard to get off easily.
Well I did it, got the bikes into the boxes: 105 x 21 x 760 Have to carry my seat and suspension seat post separately, the extra weight of the Rohloff means it's over the 23kg limit. Will be entertaining arguing with the check in in Tokyo I bet. The Rohloff was a PITA as well, you have to pull the external transfer box off to get the disc off, then put it back on, otherwise all the oil leaks out. It'll leak slowly anyway, since the skewer isn't in.
