There is an organization called Corporate Angel Network that flies cancer patients for free to accredited treatment facilities on corporate jets. The website is www.corporateangelnetwork.org. The trips are on the condition that there is an airplane going in that direction with space available when you need to go, but it is worth looking into.
Over the past few years, companies operating private jets have gotten a bad rap in the press. CAN is an organization that has operating for years, and has flown hundreds of patients for treatment with no publicity, no fanfare.