I'm a contractor and I don't take deposits on any job under $10,000 – I don't want anyone else's money in my bank account. Something doesn't seem right for them to need that much of a deposit yet still have a two to three month backlog.
On jobs over $10k or if I get a funny feeling from someone I'll ask for a one third deposit on the day we start work and the balance to be paid on the day we finish.
I would be very reluctant to give that much money upfront for work that into the store for a few months, perhaps you could put it on your credit card and then back charge them if there's a problem. Your credit card offers way more buyer protection than a regular check.