By incrementing 3 for each race the karts are always in the same relative position compared to the car in front and behind - for example car 9 is always placed behind car 8 for all 12 races, which isn't fair. One thing you can do is after race #6 flip the relative positions of each group of 3 cars. For example consider the cars in slots 4, 5 and 6 for race 6: under your scheme for race 7 they would be in slots 1, 2, and 3, but instead put them in 3, 2, 1 reaspectively. Then continue with your regular scheme. This evens it out quite a bit, though it's still not perfect because you have 35 cars, and there is no way to make it totally fair over 12 races. However - if instead there were 36 cars it would be possible to make it perfectly fair.
As for how the site works - no apology needed, as your option (b) is the way we work around here. This is a help forum, and the folks who answer questions here do it because they like to do it!