Just stumbled on this thread but figured Id add my personal experience for you. Bought a house with 25 k cash and spent 35k to renovate. we put most of the renovations on a credit card with the plan of doing a cash out refi when we completed the project and then pay off the credit card with that and have a small mortgage on the property. By running one credit card almost to the limit, it lowered my credit score from 750 to 675. Because we hadn't owned the property for 6 months there was the "6 month rule" that was limiting our options for refinancing. We found a portfolio lender who was going to be able to do it but guess what? He said our score was too low, we needed to be at 680 for him to do it. Moral of the story is carrying those credit card balances HURTS a lot. You are better off saving less and making a smaller down payment then incurring debt on the credit card, even if it is at 0% interest. Realistically if you did this strategy and went to get a loan, your mortgage guy would possibly tell you that you need to pay off the credit card balance so they can "rapid rescore" you and get approval.
Now with all of this said, you did state you have credit card with high balances. So lets say you have a credit card with 20k limit. the rule of thumb is that you need to keep your credit card balances below 50% of max so that it doesn't hurt your scores. As long as your income is high enough that 5k of credit card debt doesn't ruin your debt to income ratios, there is a good chance this won't affect your ability to get a mortgage and your method could actually be a creative way to get the downpayment money that you need.
So at the end of the day, there are essentially 2 issues to pay attention to Debt to income ratio, and how carrying a balance affects your actual credit score. If your score drops too much you may still qualify but at a lower rate.