Example, $0 balance, card limit $1k, pay onto the card $10k, card limit is now $11k.
$10k of that is really prepaid and $1k is truly credit, but it would have solved their problems given they had the cash on hand and mostly wanted to avoid declines on their cards due to draining the credit limit to $0.
The problem with other forms of payments is they're only usually accepted on a contract annual basis and you're now vendor locked for the remainder of the contract. You're also up fronting the capital to that vendor.
This sounds pretty specific to the USA. Here in Europe you certainly can rent a car with a debit card.
One thing I’d suggest doing different - instead of trying to inch up credit limits rather have that conversation at same time as the investment. ie we’re looking for a provider to park 15m but we also need a credit line/cards/whatever. The sales team wanting the 15m will push to make the line happen internally. It’s the key moment where you have leverage.