Disclaimer: I’m not a great climber, but I’m a much much better climber than I was a year ago, especially on the road. Main reason is I’ve done a bunch of climbing. And the more I climb, the easier it is to tune in to the “forces” part of the equation you mention above. With climbing, I think efficiency (technique) is at least as important as strength…and maybe much more important. I know a number of riders that are physically less strong that can outclimb me. The reason is they are better riders. I’d encourage you just to keep practicing, perhaps making hills the goal for particular rides. Also, on your last point on balance, I’ve seen really good riders climbing really steep hills, and maintaining speed wasn’t a factor. They were basically doing short still-stands in between each pedal stroke. Technique will trump gearing IMHO.
Does faster cadence help? I say definitely. If your cadence is slow, more energy goes into staying up.
…but wait, is it simply cadence, or the speed of the wheel? …or both? I suspect that the speed of the wheel is a significant factor. If the wheel isn’t spinning much, you’re probably putting more energy into staying up again.
Also, with a unicycle, there are a couple different ways of staying balanced. One way is by putting weight on the pedals. If you’re leaning back too much, you put more weight on the back pedal and it lifts you. If you’re too far forward, weight on the forward pedal with push you back. The other way to stay balanced is to move your upper body to keep your weight centered above the axle (an extreme example is BC wheel riding).
With a geared uni, you start to use more upper body since putting force on the pedal produces an exaggerated wheel movement and it can fly out from underneath you.
On a uni that is geared down, I imagine it could mess with your balance even more since when you put your weight on the pedal the pedal will move much faster than on a non-geared uni, like stepping down a step you didn’t realize was there.
I wish someone would build one just so we can study it. Maybe someone could switch the chainring and cog sizes on a penguin and let us know.
However, I doubt there will ever be enough interest in this for a commercially viable model to be manufactured.
CMW’s this weekend, Greg… and I’m going to insist that you do some 4 foot drops to flat! 
Don’t worry, I’m sure Corbin and I will follow you off the drops… we just need a little inspiration from the mighty Harper.
I’m going to be in NYC visiting the Unatics. I have to miss CMW this year. Life is tough, I wanted to come down and see all you guys again. I can land the 4 footers now. I tend to bounce like an off-balance basketball when I try 5 foot drops.
My prediction for the future of unitouring is that once geared 36ers become common distances will increase. This is a good thing as it will allow more flexibility in route setting.
As far as a geared muni goes I think a 24x3" wheel with 150mm cranks and 1:1 & 1:1.5 gears would be awesome. Use 1:1 gear for technical sections and uphills, then kick it into 36" mode for downhills and flat sections. Rad! 