True, I don’t think “skinny” is really necessary. Just lighter with good rubber!
Skinny just makes it more aerodynamic, and a bit lighter though. Rolling resistance is theoretically better with wider tires even.
This website has a nice graphical interface to see the different drag contributions. It should be exactly the same as my spreadsheet, just no cadence/wheel size comparisons.
My rolling resistance estimate could be low; it might be more like 50 W instead of 30 W, given how knobby and thick 36" tires are… However, aero drag will still be the main componen at 33kpht. The weight will increase rolling resistance, but it is linear. For your example, 70kg total vs 74g total is 6% difference. So rolling resistance at the same speed would increase by 50 W * 6% = 3W.
Definitely something that matters, and is included in the equations. However, in real life using the right tire pressure, right tire, and body position/aerodynamics will be more important for speed on flat ground; I would almost completely ignore weight.
Weight on a climb though, is of course a big deal. It is proportional to the power to overcome gravity…And gravity is taking around 200W. Even 0.2 kg of brake is worth 0.3% * 200W = 0.6 W. About 7 seconds for your road climb race time! I took my brake caliper and lever off too to save those few seconds, no reason to not use a lighter unicycle and parts… However, rolling resistance is probably just as important if not even more… the 1 minute saving I mentioned above is probably almost all in the rolling resistance. Of course, finding the “fastest” tire is a lot harder than finding a lighter component.
Now for the off topic portion!
29 Tires
I loved my 29x2.0 Marathon Supreme. It scored well for rolling resistance. However, it is a bit heavy for uphill races. It is also not tubeless compatible. It is great for turning on all my rim widths though. I like to use this for my G29 riding in general since it turns well. However, for a big trip, I would definitely want something tubeless.
Marath Supreme rolling resistance
For my ungeared uphill races, I have been using the Big One Liteskin 29x2.35. Great for most uphill races ungeared, since it is a bigger diameter. It is super light and scores extremely well in rolling resistance. I set it up tubeless, so I think this might be the lightest and lowest rolling resistance tire out there. However, it doesn’t seem to be available anymore.
Big One rolling resistance
The new G-One Speeds, which are what replaced the Big One, do not seem to score well for rolling resistance.
G-One Speed rolling resistance
The newest version (G-One R and G-One RS) use a different rubber compound, and seem faster, so maybe you would choose this instead of the G-One Speed. Maybe, they will come out with a slick version soon too…
G-One R Rolling Resistance
G-One R
G-One RS
I recently bought and used Rene Herse Antelope Hill 29x2.2" Ultralight Casing with a latex tube. Rene Herse has narrower widths, and the model name for each width is different. It should be comparable weight and rolling resistance to my older Big One. However, I have read people have problems with tire blowouts when using the ultralight casing, high pressure, and tubeless. I have not tried it tubeless yet.
However, if you use a narrower version, like 48mm, that should help with tire blowouts.
The 2.2" version does not turn too well though for me. I had it at 45psi on a 25mm internall width rim.
29x2.2 Antelope Hill
700x48mm Hatcher Pass
Rolling resistance for Rene Herse Slick Tires
If I had time and money to test for a long Guni trip in the mountain, I think the Rene Herse 48mm might be something to look into.
Rims:
I used the narrowest MTB rim from light bicycle they had at the time for my ungeared 29.
The used to advertise at 70psi max, but changed it to 40psi. I usually run my Schwalbe Big One Liteskin 29x2.35" at 45 psi tubless. There was no flyweight version when I bought mine. At 45 psi, the spokes lose a lot of tension (rim compresses). I would not go to the flyweight version on an asymmetrical disc brake hub.
Their newer 29" mountain bike rims look very nice though, asymmetric to help with spoke tension, and a little bulge so it is not a straight hookless profile. I just worry it might be too weak. They are very flexible with customizations though if you email them, so maybe if they could do a reinforced version, this would be a very good choice. 250grams, with around 100 grams reinforcement would still be 350 grams!
I use this gravel rim on my guni. Mine is hookless, and I regret not getting hooked! (On my bike, I’m happy with hookless though, since I do pinch the tire and hit the rim when I hit holes very fast) I run exactly at their max pressure rating of 55psi with a 32mm Continental Grand Prix 5000 for uphill races. A bit higher pressure would be better for sure with such a thin tire. Even if you use 2.0" tires, I think the extra reassurance will be good with a hooked version.
My G29 uses the standard weight version. My gravel bike has the flyweight versions. Again though, there is considerable spoke tension loss when you inflate the tire. I would not feel safe using the flyweight version on a unicycle, even at my body weight. It will be a tiny bit heavier than the mountain bike rims since it is a deeper cross section, but I think it looks cool 
I have emailed them about drilling the holes offset, and they said they can do it. 1mm offset is no problem. 2mm offset, and they would add 30 grams to the spoke hole reinforcement layers.