Cars get expensive fast when major parts go, and a slipping transmission is about as bad as it gets. A replacement usually runs about $4200, which hurts, but tackling the job at the first sign of slipping keeps you from getting stranded with a towed car and extra damage.
You can negotiate shop labor or source your own remanufactured unit separately from how you pay. Spreading that cost out over time keeps your savings intact while you get back on the road.
Keep in mind that a 0% intro APR for 15 months on purchases and balance transfers is a strict deadline, not free money. If you still carry a balance when those 15 months end, the standard interest rate kicks in and applies to whatever amount is left.