Only keep heavy horses for those days where you feel like wasting money. Even though I rarely use it now, I still have a desert horse and rouncey in my inventory, just in case I have a horrible time and lost huge amounts of money with my courser. I also have a Mamluk horse, but that only comes out on those times GK decide to roll heavy cav, and even then I'll only ride it 3-4 rounds if I'm lucky with upkeep.
It takes a lot of grinding, but unfortunately for cavalry the only way to be safe with your money is to have lots of options. Upkeep/multipliers can be very luck based and sometimes you'll be on the losing team for hours, or the winning one for hours.
I ride my courser until I get down to 15k gold. If I get below that I switch down. Fortunately I usually have a buffer of 30k, but if you're heavier cav using heavier/more expensive armour, you'll have to play it safe.