This is one of those quirks of the hotel industry. And it's not just Hilton...I believe all the major hotel groups operate in the same manner. You can't mix payment methods and still abide by a minimum stay requirement due to system limitations.

Most hotels would be fine with approving two reservations with different payment methods if the total length-of-stay meets the restriction. But, you can't call the hotel directly and have them make the reservation because all points/certificates reservations must by made through the chain.

And you can't call the chain to make the reservations because they would need the hotel to approve the exception. Reservationists need to be willing to call the hotel and then find someone with the authority to say yes (Reservations Manager, Revenue Manager, General Manager). That isn't a simple task. I used to be a Revenue Manager and my day mostly meetings or doing technical computer tasks away from my phone.

Sadly, I wouldn't expect this to ever get easier. If a hotel has a minimum stay requirement, it means they believe they will sell out. As such, probably don't need the one or two split-payment reservations that might happen in order to sell out. Chances are high that the room will eventually get sold to someone with a single type of payment.

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TL;DR: Reservationists need approval from the hotel to make these types of split-payment reservations. You'll need to find someone willing to make that call. And even if they will call, they need to track down someone with the authority to approve the exception. In many hotels, there are only 2 or 3 people with the power to say yes.