Watching those videos I have a few thoughts.
On the hill climbs, it is REAL important to stand up, lean slightly forward, and do everything possible to keep up your momentum. A little speed is your friend when it comes to those big rocks. Too slow and a glancing blow or trying to roll over one will put you on the ground in a heart beat. With enough speed, the bike is more stable and better able to deal with those rocks. The gyroscopic effect of spinning wheels is your friend. The standing also allows the bike to flop around a bit more without flopping you around, which makes the bike much easier to control. This is especially important on the big adventure bikes that have less suspension travel and can't go as far over before you reach the point of no return. Lastly, try not to follow too close to the rider ahead of you. If that rider has problems and you can't get around, then you might have problems as well. Stopping on a hill climb is to be avoided at all costs unless you just have no choice. It can be difficult, if not impossible, to get started again. Remember, momentum is your friend and stopping kills it
If I see a rider stalled and I have to get around him, I will continue to the top of the climb, or at least a mostly level section before the top if available, and walk back down to assist. That is usually easier than trying to stop and assist, then restart my own climb. This is especially true as the climbs get longer and more technical.
On creek crossings standing helps for many of the same reasons as on hill climbs. It also can help you see rocks under the water easier. It is usually a good idea to wait for the rider in front of you to complete the crossing before you head in behind them. You don't want to have to stop in the middle of a crossing. The rear tire can sometimes dig into a soft bottom, making it VERY difficult to get moving again, especially if there are any rocks in the way! You have lost your momentum and gyroscopic effect, which are your friends when it comes to getting around/over any rocks. It also sucks to get roosted by the rider in front if he has to get on the gas
Fatigue is a BIG factor for this kind of riding. In my experience, it has been the biggest contributing factor to accidents/falls that I have seen on many many rides (including my own). I think this is more frequently an issue than even a lack of technical skills or experience. It is common when riders are camping. Most people generally don't sleep as well when camping as they do in their regular beds. Add to this the likely higher than usual energy expenditure over a day of this kind of riding and it does not take more than a day or two before many riders start to feel the effects of the fatigue. I often try to plan trips like this to have the long days up front and try to put the shorter days at the end of the trip, if possible. Either that, or I try to keep each day short, like maybe 200 miles tops. Even if you average 25mph, that makes for an eight hour day of riding. Ideally, I would like to ride three days, take a day off, ride three days, take a day off... Now if only I had a job that let me take that kind of time off for trips!
This one looks like it was fun! I recognize some of the stuff South of Pie Town and I have been to that gas station in Datil. We too were getting iffy on gas... but they were open.