The guy that originally installed our HVAC last year says he'll be able to replace just the coils for the outside units rather than replacing the entire thing. Fortunately, the compressors and electrical components - which make up a considerable amount of the cost of the unit - are still in good shape and were probably not harmed by the thieves. He was supposed to price out the parts today and give us an estimate tomorrow. I'm sure it will be considerably less than the $3850 that the other contractor quoted. Having to pay anything at all is not ideal, but our insurance doesn't cover it. (Since our house is incomplete, traditional insurance companies will not insure us. We have a government-underwritten plan called the Ohio FAIR plan, but it doesn't cover theft.)
To prevent this from happening again, we've talked about different security measures we can implement. Our former insurance agent, who now owns his own security-system company, dropped by the house yesterday and said that it would be easy enough to hook up the air conditioner to the house system. We also talked about setting up cameras for the side yard and alley. We might still do one of those, but neither would necessarily prevent another theft, only make it easier to catch the thieves. Tom found this product that seems to be a pretty economical solution.
Provided that it does what it claims, a couple of hundred bucks is a small price to protect our investment.