Strictly speaking from my own experience flying with a horn:
I've been flying with my euph (a York Preference 3067, basically a Besson Sovereign 967 for the purposes of this discussion) for about 5 years now. I have a cordura Cronkhite bag that I've been using to carry the horn on, and I've only flown on Southwest airlines as I have their rewards program, and I know for certain my horn will fit in the overheads on both the newer 737 aircraft and the slightly older models you sometimes still see.
My horn's bell is about 12 inches in diameter, which is slightly bigger than the Yamaha Neo 642 you have (Yamaha's website lists it at 11 4/5 inches). So, if you use a Cronkhite case with your horn it should fit in the overhead on Southwest's aircraft. They also only use those two models of 737s regardless of the flight distance.
As a side note, the newer 737s have a bit more space in the overhead compartments, so my case fits even easier on them.
Regarding the Cronkhite case specifically, in general the normal (non-M5050 design) should fit most models of pro euphoniums you would probably be in the market for, and if it turns out to be too small you can sell it like what Dave mentioned and probably make a fair amount of what you paid for it back so you could get the M5050 size.
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)