A couple of thoughts:

(1) as a business owner I would be very wary of a perpetual cut, so I would cap it.

(2) since you're capping it you can demand a larger cut to ensure that you're repaid faster.

I would propose something that would enable you to earn ~2-3x your initial proposal cost over a period of approximately 1-2 years. Ultimately you're giving them a loan. This is "owner financed software development". Think about it in terms of interest rates and the cost of money, not in terms of becoming their partner.

Furthermore, you might find that you can secure collateral for your loan. For example, they agree to pay you over time and secure that opportunity with you by making you a secured creditor on their books.