I'm in the same boat, it's very difficult when they are persistent not to blert out a price. But whenever I do, even a reasonable one or a broad range, they are as good a gone.
In the main I just ask back some questions like Do you know whether it has a wool content, has it been cleaned before, etc then pause.
Then say I really need to see it to give you and accurate quote, any Professional would want to see it first, you can understand that now can't you?
I've had a few agree then ring up and back out so maybe I'm wasting my time but I think in the end you get more out of your responses.