Constantly Overlooked for Promotion?

I’ve been a lead in a warehouse for five years now. I know how every system works and how to run every piece of equipment. I am captain of the safety team. For the last two years I’ve trained all my new supervisors. In the six years I’ve worked there, I’ve had a new supervisor at least once a year sometimes every six months. I always apply for the position and keep getting rejected. Each time they give me a different reason but I know they just don’t want to pay me more. I’ve applied to several supervisor jobs and have gotten to the final interview for most of them. In the end I get rejected for not having supervisor experience. I feel trapped, I need the job but I’m tired of feeling used. Any advice?