Saddle height for MTB might need to be a bit lower... I'll skip being the expert on that though as I've heard all sorts of preferences...

Your balance steps in greatly here, how slow can you ride or how long can you stay upright when stopped; how much front tire popping up during that climb can you handle. That doesn't answer anything, but obviously it helps. For some more tangible tips (adding to your list).

Black scenario: yup, just too steep to start on. It's a fact that we can ride steeper than we can start on.

White scenario:

• Pedal at 2 o'clock: yes, as high as you can tolerate it. Maybe even 1 o'clock, as you be a bit back on the bike (only so far back that there's still some weight on the front for steering). The front tire may very well come up as you do this, don't worry and save the steering for when the wheel is actually touching if you can.
• Choose a place with some traction if you can. Wet tree roots are not the place :) In fact, note the next few good traction spots... and also the slippery ones.
• Don't choose a gear too low, you won't get enough umph out of one stroke to stay up on, and it'll be harder to ease into the torque. You want to be putting all your weight on it, and pulling with bars too... one gear higher (or two?) than what you might use had you not fallen off. That will move you a bit farther on one stroke, but you'll have to push hard and be ready for the end of that first stroke (the dead spot is longer too!)
• As you do that stroke, transition your weight forward. Forward weight is not what you want, but by transitioning forward you're pushing on the back tire. Aim to be slightly forward when you end your stroke. Imagine you're pulling the weight off the front wheel , and that action leaves you slightly forward at the end of the stroke.
• Near the bottom of your stroke, when the torque is rolling off flick the bike forward with the handlebars to get you through that first dead spot, this will take a lot of shoulder action. (I've also seen guys do a quick 90° back pedal into that 2 o'clock position again, rather than fumble through the dead spot;). If your trail is ridden with tree roots and slippery spots you can also use the quick back pedal to align your dead spot with that tree root, and flick over it.
• After a few strokes and some speed you might be able to coast for one pedal and shift back into a lower gear, and you can call it a successful start.
• If you really want to improve your chances of starting, take a quick 1min breather; take a drink and a wiz. You'll need to be ready for putting in the sprinting effort required to get started again.

Along with what @Michael has stated a technique I use is to find a rock, tree root or other obstruction to keep the rear tire from sliding downhill. With the front brake applied start to pedal. When you have both feet off the ground and on the pedals release the front brake and start to pedal smoothly. A stroke that is too quick will re3sult in the rear tire beginning to spin and result in you being stopped again. It is a technique you can practice on the road or less technical incline. The key to making it work is a smooth yet powerful consistent pedal stroke.

One trick that I've been trying (but not quite perfecting...yet) is something I learned from motorcycle racing: brakes aren't just for controlling wheelies, but also wheel spin. It's a manual form of traction control! So...when trying to restart on a loose uphill, besides the other things mentioned here, I've been toying with controlling the rear wheel spin by modulating the rear brake as I apply power to the pedal. The more I feel I've got the weight back on the tire, the more I let off the brake. This still requires some practice, but it has shown promise so far. I feel the front brake method mentioned above still allows for the rear spin that kills much needed forward momentum.