Remember the expression, "Loyal Customer"?
Those are long gone, and so is the expectation that a new customer will be as good a risk as a current, proven customer.
Successful companies grow by accident, and have measures in place to take care of current customers before they take on new customers. Sounds fair to me.
Just an observation, here. Perhaps a little advance research into the local contractor base would eliminate some of the choices, without alienating the rest. Then you would already know whether or not you hoped that they would submit a bid to you.
Contrary to popular belief, new customers aren't always a blessing to a contractor, in view of everything involved in not losing money being in the business.
Customers need to be weeded out, just like contractors do. It's NOT a one way street.
If you want a company to be loyal to YOUR needs, what do you offer them back, in terms of loyalty? In terms of flexibility?
You ARE an engineer, as well, aren't you? Just a hunch....