Who should I have rescheduled?
Since you already had a scheduled interview with the small company for that time slot, you should reply to the very competitive company immediately, telling them that you are sorry, but that you are busy at that time and offering an alternative time.
That's just common courtesy.
As @RobinBennett wisely pointed out in a ...
It makes no difference who to ask to reschedule based on what is easier for them.
You base decisions on yourself. Whichever is most likely to land you a job should be prioritised. Or whichever has the better position for you. Either way base it on your needs.
It might feel right to reschedule with the competitive company because you agreed to the time with the smaller company first however it depends on which role you're more interested in.
If a role with the competitive company is more attractive (and let's be honest, they're more likely to be difficult to reschedue with than the smaller company) then I'd try ...
Best answer here is just to start the conversation with your boss. You've made some good points above about why you think it would be beneficial to WFH as well as suggesting that it would be a help to the company if your salary switched to hourly.
It may be that you don't need to become a contractor as such (this has it's downsides) but a renegotiation of ...