At Willamette we don't use plastic wheels of any kind. Our tracks have too many corners and pot holes and they tend to break to easily. I buy 48 spoke double wall BMX rear wheels and as long as you tighten the spokes tight before every race they do great. Occasionally we might break a spoke but almost never have a full wheel failure. We use a number of BMX freewheels I just let the bike shop know I need very tough ones. I buy 16 tooth ones so I can mount the sprocket with 4 bolts evenly spaced. For our rear sprocket to mount to the freewheel we buy 'blank' 35 pitch aluminum go cart sprockets with a 1" hole in the center. We then mount these on a lathe (a little hard to center but can be done) and machine out the inside hole so that it is a snap fit for the freewheel. We then drill 4 1/4" holes in the sprocket that sit inside the teeth of the sprocket These need to be fairly close to the freewheel body but not so close that you can not get an altered nut and bolt in the hole without touching the freewheel body. I like button head bolts as they use an allen wrench to tighten and can grind off some of the head if needed to get into the hole. The head of the button head is on the machined sprocket's side. On the freewheel teeth side we use a washer that has been flattened on one side so that it fits up close to the freewheel body and if needed we can flatten one side of the nut and reduce the diameter of the button head's head so that it can be turned. If the hole is too far out it will break off teeth from the freewheel and not stay tight. This is a very cheap system and it teaches the students more skills and works great for us.

My school doesn't have a lathe, we do have another machine that might work but Bluesky has carbon fiber wheels, even with a lot of castor do you think they will work? But for a rear wheel this looks great. Our car was made about 6-7 years ago and when it was made the original team did something very similar to this on the four wheel car... the problem was the sprocket was cut wrong making it roll like an egg, somehow it worked but I think it was mostly luck, I still don't know how we finished the season with it.

If the rear sprocket is not cut out dead center the chain will get tight and loose as it goes around. We have some that students have not centered well and they will work. I have them adjust the chain so it is fairly tight (about 1/4" flex with a slight push) on the tightest place and then it is looser on the other side but if your rear mounting system and motor are mounted so that there is no flex then you still will not throw a chain. I leave mine so it has about 3/4" of flex at all times even though mine is centered so there is no drag on the motor bearings by having a tight chain. I have not thrown a chain in several years and that was because I did not tighten my motor sprocket tight enough and it moved.
Good luck,
Mike