Typically when you are moving debt to a credit card, you are not making a purchase, but are withdrawing cash from the credit account to pay for the LOC. A cash advance usually means you are paying interest on the amount withdrawn immediately at super high credit card rates. There is usually no grace period given for cash advances. IIRC, the cash balance is tracked separately from your regular card balance, and payments first go to paying off the normal monthly balance, and when that hits zero, they go towards the cash advance balance. That keeps you paying high interest for longer if you can't pay it off in full. You'd have to read your terms of service to confirm how your card handles this. Be careful to make sure you understand your terms.

There are frequently special balance transfer offerings issued by card companies that allow you to transfer your credit balance from one card to another for a fixed initial cost (3% of balance seems normal now), and then you get up to 12 months at 0% interest. That can be a pretty good deal, but you would have to confirm if you could do a cash advance on one card, then balance transfer to a second one using a promotional offer and make sure the second card doesn't still treat it as a cash advance balance, which would likely be subject to immediate high interest rates. This is probably the most likely scenario. However, if you can confirm they treat the transferred balance as normal, it would end up being cheaper than a year at LOC interest. Then you pay it off in full with the LOC and repeat, assuming you get another offer. I think it is more likely banks will look out for each other and that won't work for cash advance credit card debt, but hey, maybe there are banks that just want your business and only a little cash instead of a lot.