A common way to deal with such optimisation problems is to create a scoring function which combines the variables in such a way as to generate a single number which can then be used to sort.

Looking at your challenge, it would appear that there are some factors which are multiplicative such as chances of gaining a winning position. Others are additive/subtractive - the value of the transport costs should be subtracted from each of the prizes to give an overall profit and this simplifies the calculation. Factors that positively influence the outcome should be additive/multiplicative while those which make it less attractive should be subtractive or used to divide.

Splitting the calculation by day (so the two days of a multi-day event are separate lines) would avoid extra complexity.

My advice would be to include a number of weighting factors which you can manually adjust to see if the ranking produced looks sensible.

I hope that is useful. I must admit that I seeing a question from a rodeo rider from a city called Great Falls did bring a smile to my face.