MS to shake the 0% offer:
Card A - statement cuts 1/31 due date 2/25 $3k balance on this card
Card B - statement cuts 2/10 due date 3/5 no balance
1/27 - MS on Card B for 3k, use BB or MO to pay off card A by 1/30
1/31 - Card A reports zero balance
2/1 - MS on card A, use BB or MO to pay off card B by 2/9
2/10 - Card B reports zero balance.
Notice how the due date doesn't matter for this purpose.
Rinse and repeat until you get an acceptable 0% offer. I would not continue this for the long term while carrying a balance. If you end up with an unexpected big bill like taxes, you will not have the ability to MS your way out of it. In general, MS with debt is bad. All of this is with the caveat that a real job pays a lot more than MS with unusual exceptions like the OM deal with Ink. If you can run around getting gift cards, you should be getting a real job unless you have a disability. If you can get a business card, you can MS the balance to it (if the current card with the balance has a high rate) and then wait as long as needed for the 0% to show up. You should apply for the business card when your credit report shows no balance due to MSing back and forth. That will give you the ability to move the $3k off of your credit report temporarily until a 0% offer shows up.
The bottom line is to pay off the $3k ASAP. Get a second job. If that means converting UR to cash at 1CPM, then do so.