I agree that shorter cranks don’t always result in faster speeds.
My 26” Nimbus II road unicycle has 125mm cranks.
My fat tire Large Marge 24X3.5 unicycle (26” diameter tire) has 140mm cranks on it.
I apparently spin faster with 140mm cranks than I do with 125mm cranks, because I ride the fat tire unicycle 1 mph faster on concrete/pavement, over the same route.
exactly. that is why I have so many wheels. With all at 150mm, the wheel makes the uni go faster. I still prefer 150s over 125, but I can also do with 140s.
There is no single best size for any wheel.
Crank size depends entirely on the strength of the rider compared to the maximum gradient encountered. Same as with any engine. Too high geared and you stall. You can sacrifice gradient for more maximum speed but I find it is boring to walk up hills.
The key is to have several unicycles, each set up for particular routes and selected depending on whether you feel like serious hill climbing on the day.
Exactly you should have all size unicycles both in road version and in muni version and a separate shed to keep them all in. I am only halfway there.
My knees have become an issue for riding uphill (and downhill). luckily there aren’t any big hills around here anyways.
Being out of the uni progress for so many years until I was covid bored and landed here, very nice!
Seeing disk brakes, handle bars, gears, big dia wheels got me inspired.
BUT,
Prices also have changed…
So started searching used online.
Found a 28 cheap not knowing that 29 mtb tires would fit, cool!
I learned why cheap even though uni.com new was left outside to rust!
I spent a LOT of time getting most every part taken apart, torch, wd 40 ect. Seat hard and dead.
Pedals not worth saving but wheel tru enough.
Seat post to short quick release way gone.
As I started muni on a 24 miyata in early 80s was excited to see difference. Came with 150 cranks. They were ok for about a week, felt to long.
Oredered new seat, post, cranks, 127 and 107.
My miyata had stock 140.
After getting 95 % free mounts down and idle both legs using 140 decided to try 127.
I am 64 now in pretty good health, mtb and kiteboard tons.
But 127 was much harder to free mount as seat higher like pedals.
There is a short incline nearby can climb easy with 150, 140 but much different 127.
So after about 2 months put 140 back
On 29 and 127 on 24.
As got a maxxis used tire way enough friction
so offroad. HUGE difference from what I recall 24.
But found out why brakes for downhill are nice.
This summer will again try 127 on 29 and 107 on 24.
I must say bravo for all using short cranks on big wheels, for me maybe never, higher speed crashes scare my body!
55-75mm. But maybe a bit longer for grades steeper than 40%. 
55-75mm on a 29”? Maybe one day for me. Maybe. (Who am I kidding? )
Currently, my 29” road uni has 114mm cranks, and that feels short and fast enough.
@PedalSprell @Setonix @vtunicycle on my 29er genarally I ride with 125mm on tarmac and find thats a good compramise for the older rider. I can ride the 100mm and like the smoothness, but its a bugger to stop and less control. 114mm I havent tried on the 29er, but have tried on the 27.5 again ok on the road.
If you want to test them out then suggest Qu-Ax lightweight ISIS 114mm cranks are not expensive.
Then if you like them you can get some better more expensive ones. You can buy 3 or 4 sets of these for the price of 1 Nimbus or other brand.
I have tested 2 sets the QuAx 100mm and the 114mm and been riding these for a while vs my other unes with Nimbus cranks an they seem just as good, and a fraction of the cost. They come in a range of sizes but defo 125,114,100 and lower.
Yesterday I ordered a 29er with 114mm cranks. The largest wheel size I’ve ridden was a 27.5 Oracle with 150mm, and that seemed fast to me in comparison to my 20er. (The 27.5 was someone else’s, I only rode it for a few minutes, and I ride my 20" almost every day.) I hope I ordered correctly.
I’ve thought of getting a 27.5, but someone on here said he hated it, coz peeps couldn;t make up their minds in getting either a 26 or 29, which I actually have. I don’t expect big difference in 27.5 vs 29. Prolly also depends on the tire that is put on it, so I won’t be getting a 27.5. The one I really want is a 24" muni.
You will come to like your 29". For me that is just the right size, even though my last few rides have been with the 32". If you think the cranks are too short, you can always get longer ones again. Short cranks are mostly a problem with mounting I think, well and stopping too, if you don’t have a brake.
Don’t forget to show a picture when you get it.
The 27.5 seems like a really nice size. It was pretty fun to ride, and maybe that’s because it was my biggest wheel yet, but it easily went over grass and roots and steep hills, and I felt really high up. In the future, if you’re wondering what uni to get, maybe get the 27.5", I think it is the only size you don’t have, right?
29/114mm is one of my favorite setups, although it might feel a very short or heavy if its steep or if I am tired. (I have reverted back to 29/125mm and im super happy with that now.) I hope you get used to it quickly and are strong enough to go everywhere with it. I hope you got brakes with it, although you would probably manage without. Good luck! 
Unless you have a safe and sheltered place to store your new uni at school I would advise you to consider keep bringing your 20" to school if its not that far. If it’s only a km away or so the time difference is negligible anyways.
Anything bigger than the 20" would not fit on the bus. Don’t worry, the 20er will be used.
I did not order a brake with the uni, though I want to buy a cheap hydraulic disc brake from amazon for $25. Is there a big difference from that and an expensive one?
you can also use your hand on the wheel as a brake. That is even cheaper. I would give you a medal for that. 
Hey, that‘s my territory! How comes you ride such long cranks?
I‘d love to try 120s, but am not aware of them existing, or where to buy them. 114s are prolly a bit short for me, plus they are at home on the 20er anyways.
The KH Moments and Spirits had a 117mm option (in single or dual) but are no longer in stock except in UK (not for long).
They have such high Q factor… @Wheelou is better off drilling/threading a 120mm hole in a pair of 150mm cranks.
I think I even have 117mm KHs (I bought a dual hole 137mm KH to some day go on my Schlumpf. Not sure if the second hole is 110mm or 117mm). But I have to agree with @PedalSprell; the Q factor is a bit of a problem for me. It‘s the reason I bought them for the Schlumpf, since they keep me off from accidentally hitting the knob with my heel. But except for muni I‘m a 100mm bearing spacing, no Q rider. Plus 117mm is already pretty close to 114mm. I‘m fine with that on the 20er, but doubt I could handle it well on a 29er (actually, a 28er, but still).
Drilling and threading a set of longer cranks seems a reasonable idea. All I need is a set of the right taps.
Anyway, thanks for chiming in and offer a possible solution.
Knee pain… Better to ride long cranks and a go bit slower than to get occasional downtime on my riding. On the flipside: I can simply do more fun things anywhere. Honestly, riding 125s now feels pretty much like riding 150s did back in the days. Do anything anwhere. Except for really technical stuff.
I will eventually go back to my 29" with dual hole 110/130mm setup, though. 110mm for getting somewhere and 130mm for Muni and general shenanigans. But right now, 110 is to sketchy and 130 mm is to slow. 125mm is a good compromize.
Those dreaded knees…
Good luck on your plan to go for dual cranks 
…and make sure to not accidentally mount them on the wrong side! 
I can relate to that; I now ride 150s for muni and can do the same stuff (and more) than I did with 165s a year ago 