Driving a manual means dealing with the inevitable day the clutch finally slips and refuses to grab. Between the parts, the labor to drop the transmission, and the machine work on the flywheel, keeping your car on the road isn't cheap. Late fall is the best time to book this job because shops slow down before the holiday rush and are more likely to deal on labor.
Negotiating the repair bill has nothing to do with how you pay for it. Get a firm quote that breaks down the parts and labor separately before you mention financing. Once you have the final price, you can figure out how to spread the cost without letting a shop run your credit for their store card.
Remember that the 0% intro APR for 15 months on purchases and balance transfers is a hard deadline, not free money. If you still have a balance left when those 15 months are up, standard interest kicks in on the whole original amount.