You might be able to negotiate with the medical provider itself. Say you want to pay without insurance and ask about the cost and doing any reductions.

The number on the bill before the insurance discount is entirely imaginary, no one pays it.

There is always a built in cash discount for people without insurance.

For example, for a while I was having trouble getting insurance cards (stupid reasons) at a new position so I was paying out of pocket for prescriptions and office visits.

They were less expensive paying cash than with insurance pre-deductible.