Towing a trailer puts a lot of wear on your vehicle, and keeping your brakes in top shape is the most important part of the job. Shops are usually less booked in late winter or very early spring, so aim to get your quote before the first warm weekend of the year hits and everyone else rushes to the garage.
Budgeting $550 for the hardware and labor is a safe bet, though custom wiring can sometimes add a little padding to that final bill. Don't worry about negotiating the labor rate too much, but always ask if they have a preferred brand of controller that might save you a few bucks on the initial purchase.
Remember that this 0% window is a deadline, not free money. If you have any balance left after those 18 months, you will start paying interest on the remaining amount immediately, which can quickly undo your budget.