Brian
I had this a few years ago. I paid both weeks together, and subsequesntly received a late charge. When I called about it, they found that the two payments had been credited to one of the weeks, and the other showed no payment. It took several phone called and progress up the lader of responsibility before I could get them to appreciate what they had done and credit back the late fee.

Just perservere and keep phoning.

The check cashing project is farmed out to an Atlanta Bank that dos not know what the timeshare is like.
It's processed as any check for payment would be and therefore they have problems with it when you pay for different units with one bill.
It's a deal by Hilton with the bank to process Millions of Dollars through them which is another way to get discounts by Hilton.
I have had problems many times and realized it has to be presented so any teller at the bank can handle it.
When you introduce multi payments in one they just louse up.

I think the maintenance bill asks for separate checks for each week you own and that may be the problem,as they do not like to co-mingle funds
I had a similar problem on late fees but had fortunately registered the envelope
The payment was with a US Funds Bank Draft purchased in Canada and was able to provide proof they received it on time so the late fee was reversed.
In previous years I always paid by credit card,and had no issues,so next year I will be using credit card again as it just seems to run more smoothly

I am sorry to hear of these issues, and that the proposed solution is to pay by credit card, because it costs the association money when owners pay by credit card. Like every other business, the credit card companies charge us a fee every time a credit card is used - and we certainly have better ways to spend owner's money! I wonder how much of a problem it is? It is worth looking into.