I've only flown once to hunt, last September. It went very smoothly. I've flown a whole lot for work, had some harrowing experiences there. I will share some of my tips and answer your questions:
1) As the other guy said, no, your 26" frame won't fit in most overheads without pissing people off and putting it in horizontally. If you want to do it this one time and piss people off, that mentality is pretty common these days, so when in Rome I guess.
2) I would recommend reversing what you plan on doing - carry on your optics, electronics, anything expensive and irreplaceable like releases, contact lenses, medication etc - carry those on. Put in checked bags what you can afford to go to the store and replace in a pinch - clothes, toiletries, camp gear etc.
2a) Consider shipping essential gear if you can send it to an outfitter or friend. That way you can send it in advance and know it is waiting for you upon arrival.
3) I've lost three bags in my day, and eventually gotten all back except one. One was delivered the next day, the other took about a week. Plan like it could happen and hope it doesn't. Amazingly all three happened on the way home so I was ok. Pay extra to connect through better airports. There are good airports and bad airports to connect through. My issues arose in Philly twice, and Atlanta once, both airports are massive with reputations for being generally shitty. Most of the really bad ones are on the coasts, so you shouldn't have too much to worry about being in MO. Direct flights are much less likely to result in lost luggage.
4) Have a plan for the meat. We ended up driving a few hours to take my elk to a butcher near Boise and he was great. Cut, frozen, shipped and it arrived at the Pgh airport no hassle, no worry, for about $500 bucks including shipping. When I kill something at home I like to cut the meat up myself, but the logistics of keeping meat cool for the duration of our hunt, then getting it on a plane with all our other gear and then having to deal with it when we got home just wasn't appealing. You'll need to find a butcher near an airport to get decent shipping rates.