I think the reason they don’t is that the credit card companies charge a fee which increases with the amount charge for each transaction.
I think they would allow it if you opted to pay the credit card fee.
With my very first timeshare resale contract I did this and it worked fine. This was however not
DVC but still a title company was used.
Some companies allow you to increase the down payment instead of ie $1,500 you can put $6,000 as the deposit.