Towing over mountainpasses a problem.
 

I have the not shifting into a higher gear problem. I turn off tow/haul and the exhaust brake and then it finally shifts up. When that doesn't work I have to change the gear shifter to M (for manual) mode and then shift to a higher gear. I can avoid all that by leaving tow/haul off and using manual shift mode (exhaust brake is still enabled).

I can't help you on the overheating issues. I'm using 5w-40 oil (Valvoline PBE full synthetic). My engine oil temp will get into the low 240's pulling my 11K travel trailer up 11,000' elevation mountain passes.

Look at the specs on your particular model, towing package, etc. I would be surprised if your not overweight, No, I'm not part of the Internet Weight Police Squad.
Your gearing may also be an issue with pulling that much weight up those kind of hills.
I have read here on FTE that some have had to pull over when going up mountains or when they got over the top and let the truck idle and cool down.

Not enough truck for that trailer. The truck is overloaded by weight and that gear ratio is a killer also. For that weight you would have been looking at a f350 DRW with 4.10 gears.

Are you pulling steady/long up hills or up/down, followed by up/down where you're constantly shifting/revving, etc? That will build a little more heat than just steady/long pulls. We have just over 5 ton fiver and 2002 diesel and I've only seen my coolant temp move a couple times...never enough to make me concerned. Once was very curvy/hilly with shifting and the other was constant up/down in the 8000ish ft area for elevation.

Might want to verify you have an overheating problem and not a thermostat or a temp gauge problem by checking temps with a IR gun or hand held probe. Also check the simple stuff like clogged air filter box (I've seen mouse nests in daily driven cars/trucks), fan function, etc. Are you using a lot of bio fuel (less power than dino-fuel)? You're pulling more than me though you have a newer truck and lot more grunt so I expect a bit more. Won't hurt to check it over.

Wait so the engine is not overheating? What's your delta between the EOT and ECT?

What was your oil temp if it was in the 240s that's seem to be the norm on long climbs. Which oil type are you using?

The truck's gearing is not ideal, but using manual mode keeping the engine speed a bit higher should help. And, there is no crime in going a little slower.

I'd be comparing notes with folks at rest areas with similar rigs. That will confirm if you're getting expected performance from your rig and maybe some ideas on how it may be improved.

Long shot...does your truck have any modifications from stock?

Also, depending on configuration of truck ford's recommended 5th wheel weight is 16,000-16,500# and GCWR 23,500#.

Before you go spending a bundle of money on gears, I would check out some other things first. 246° F isn't much outside the range I'm seeing in my truck and it hasn't complained yet. No loss of power that I can tell. You're pulling at least 5k more than I am so 246° F doesn't sound that bad. But if you're losing power and the truck is telling you that then maybe something is out of sorts.

Things to check:
Clean engine air filter. I changed mine at 10k miles and it looked nasty to me, but forum members said it looked OK.
Properly working radiator fan - you should be able to hear it since it gets quite loud
Engine oil is at the proper level
A/C is off/on? I try to turn mine off before a climb, but I've forgotten at least once and it didn't seem to make much difference. Still...
Clean radiator? I know you said the coolant temp is OK, but keeping the coolant system working right will help keep the engine oil temp from being a problem. Dirty radiator fins will reduce air flow not just to the radiator but to the engine also.
Is it time to replace the coolant? When was it last tested?

Are you seeing these high temps consistently? If not, I wonder if maybe you were going through a regen at the time. That might explain the loss of power.

At 247 you should get a reduction in engine power, also 15w40 isn't approved for severe use per Ford only 5w40 is.

My '16' is a dually with 3.73 gear pulling 16,000#+, gcw 25k+. I've run over many of the passes in CO and a few in other states that twist some and have seen the oil temps climb 248f then drop to a lower temp. Just because they're diesels doesn't mean you have to take the mountain at max speed and yes there will be times that your truck will seem like it's working so slow down and enjoy the views that's a lot of weight behind you.