From a machining point of view you're best served with access lathe and mill (CNC probably needed for the nicer, lighter designs) while access to waterjet/laser cutter will make some of the machining much faster and simpler.
To get the all the gears and sprockets lined up and keep the keys in you just need to cut some bushing that are the right lengths to keep everything lined up.
From
McMaster we use:
6391K215 1/2" ID Sleeve Bearings (custom cut these to length for vertical and upper horizontal shafts)
1570K43 1/2" Keyed Aluminum Shaft (for vertical and upper horizontal shafts)
5911K42 3/8" Aluminum Shaft (for lower, wheel, shaft)
Small PVC or sleeve bearing for the 3/8" shaft
The vertical shaft comes down through the middle of a turned piece guided by bearings at the top and the bottom which keeps the shaft lined up with the upper horizontal one. If you are transmitting power form the upper horizontal shaft to the wheel via #35 chain then that alignment isn't too critical, but the bevel gear spacing needs to be more carefully adjusted with the custom cut bushings.
Don't get discouraged, but crab drive is very resource and time intensive, lots of CAD work before you start cutting with reduce mistakes and simplify your design... There are 21 machined pieces, 8 bearings, plus shafts and spacers in each of our wheel boxes.