Toss up between like a CRF250f/XR250 and the Yamaha WR250R I'd say.
Hrmm... if you know you're going out there together with others... EFI would be better performance, more consistent performance at higher-elevations because it has EFI so can adjust for air density.
If I was going far-in alone though? I dunno... I suppose EFI's by now are reliable, but I just might instead consider the carb'd bike just so less stuff to possibly fail and strand you.
If possible.. I'd want a bike that can either kick OR eStart with magic-button. But for a 250 4-stroke, the kick wouldn't be anything to be concerned about.
Electric Start is soo lovely though and can save your butt sometimes if you end up killing the engine in a precarious place on a tight single track goat trail.
If you do get a bike that is eStart only... and if it has a key? Like a DualSport model would...
MAKE SURE you get wiring diagram and study it at home to learn what you'd need to do in order to hot-wire that ignition switch in the field, just in case you have a crash and it takes a hit to the instrument cluster and that keyed switch gets damaged! Had that happen to me while doing some track-riding on a Suzuki DR400S that I setup more for off-roading. Ended my riding real quick that day.
I bet the Yamaha WR250R (<-- the DualSport model they sold here in the US and just discontinued selling here like a year or so ago after about a 10 yr run of them) would be an excellent choice for you for this application I think.
Won't break the bank. Has EFI. Has aftermarket support so you can get an On-The-Fly ECU programmer so you can change the fuel mappings for different power characteristics on-the-fly out in the field. The stock exhaust is stupid quiet. But you can shave lotta weight if you toss it and get an aftermarket. And..since it's dual sported.. you'd likely be able to take it a few more places than you could an offroad only registered bike.
Also since they were DualSports... there's already buncha after market racks and stuff people make for them. I remember there's also a lowering link for the rear suspension some company made. But I seriously seriously doubt you'd need it. It's only got like 10.6" suspension front and back, so won't be as tall as a MotoX/Dez/Enduro specific race bike.
Remember you're going to have a lot more weight strapped on you while riding it, so it'll squash down more than usual. So I highly doubt you'd have problems dabbing a foot down here or there as needed though.
ALSO... it already has lights! If you're hunting on the bike... you're for sure going to need lighting for the ride back out, like if you end up taking the shot at last light. So wouldn't have to fuss with potentially getting the Stator re-wound for more output to run the lighting. Like you might have to do on a trail bike you buy without lighting initially.
I'd also say swap out the stock battery for a lithium one. They weigh a good amount less.
I really wouldn't worry to much about your height and all that. I'm 5' 11" but only have a 30" inseam and got my start riding big tall Huskies back in the day w/ 40" seat-heights!
Also for this application, I'd probably go with a solid "mousse" inner-tube like the enduro guys run so you don't have to worry about pinch-flats from hits on rocks. If you need the ride of the tire to be softer... those guys just end up perforating that mousse tube uniformly all throughout it to modify it's stiffness. And I think you can also buy ones with different comparable PSI-like ratings to them.
MAKE SURE you get a good bash-plate for underneath! To protect the engine cases from somehow taking a rock to them and cracking on you way out in B.F.E. far away from help!
Also research how to affix a length of cabling between frame to tip of rear brake pedal to help avoid getting weeds and debris snagged in there on the trail.
Also get one of those spare spark-plug holders that you can affix to a frame member with a hose-clamp. Not as much of an issue when it's not a high-strung two-stroke... but still you should NOT go way back in there without an extra spare plug.
You'll also need a tool-roll/tool-kit to take with you so you can deal with things like changing a splug out in the field. Mini-tire spoons for changing out an inner tube if you don't go the mousse-tube route. etc.
Before you even go out riding it the first time.... go through all the plastics (especially front fender!) and make sure all the screws are Blue-Loctite'd in place! So they don't vibrate out on ya in BFE.
Oh... another important thing... if it doesn't have a fairly easy pull on the clutch lever... then replace the clutch-cable with one of those nicer TEFLON-lined ones. Back in the day Terry-cable used to make 'em. On slow-going trails... with all that extra weight you're gonna work that clutch hand... A LOT!
A pic of a Yamaha WR250R
My last beast (KX500!) before bulging discs made me have to stop.