How about writing a JIRA plug-in. You can find an area where it is lacking and write a plug-in for it.

Alternatively, start with an open source bug tracker. But offer to host it, and create improvements for it. It's been a long time, but you can set up something like bugzilla. (There's probably a more modern alternative out there).

Here's another idea. Start ups don't have a lot of money, consider receiving equity from the start up every month. Instead of a monthly rate, you receive shares every month. You will probably need a lawyer to set up this contract and there is probably a problem with this idea. I don't think you can receive ISOs, unless you are an employee, so they might have to hire you too, while they are using your bug tracking service.