It sounds like you are looking into expediting for the first time. Expediting is unique in the trucking industry. To better understand it, you might want to read
Introduction to Expediting, as well as continuing to read the Open Forum.
The fleet owner wanting you to pay for significant repairs (not $3.00 light bulbs) is a red flag for me. There are numerous stories out there of drivers that got burned because they laid out money for truck service or repairs, and they did not get reimbursed because the fleet owner was either not able to pay, or because the fleet owner disputed the price of the repair, or because the fleet owner did not agree the repair was needed.
Payments for repairs can be made directly to vendors by several means. Many fleet owners use these means to pay service providers directly, and they offer the same 40/60 or 60/40 split other fleet owners do.
It is not in your best interests to use your money to keep a fleet owner's truck running that the fleet owner is contractually obligated to keep running. The fleet owner's money should be used to keep the truck running, not yours. You are the fleet owner's independent-contractor driver, not his bank.
Regarding the 40/60 v. 60/40 decision, Diane and I contract with FedEx Custom Critical and previously drove fleet-owner trucks with the same carrier. We are familiar with FDCC's fuel surcharge program and have run under both arrangements with different fleet owners. There is no doubt about it. If the fleet owner is paying for the fuel and keeping the surcharge, you are in an arrangement that benefits the fleet owner more than you. If the driver is paying for the fuel and keeping the surcharge, the arrangement favors the driver.
An important benefit of the driver paying for fuel is it provides more freedom to deadhead 500 or 1,000 miles to get home if you have to. If the fleet owner is paying fuel, things might get difficult if he does not feel you should deadhead that far on his fuel money for personal reasons. If you are buying the fuel, there is still wear-and-tear on the truck to consider for personal deahdead miles, but the fuel issue will not rise.
Regarding minor repairs, a fleet owner once surprised us by handing us $500 cash the day we started with him. The money was to fund minor repairs. When a minor repair was made, we sent in the receipt and he reimbursed us the cost. When we left, he collected back his $500 out of money owed to us. That was fine, since we already had the $500 cash in our pocket from when he gave it to us the first day.