Just a thought about the flat rate pricing. I have similar issues in my businesses since I can't give an accurate estimate of the cost without knowing the details of a project. However over time I've realized I can give a fairly accurate range of pricing for all but the exceptional cases. What I've been doing when someone asks for an estimate without providing much detail is give them the general price range, with the explanation that the details will be necessary for a true accurate price and a commitment from me to work at that price.
You might be able to do something similar. While you won't be able to offer an exact price without checking for yourself what really needs to be done, I wouldn't be surprised if you could come fairly close based on the home owner's description of the problem. It won't work in all cases so you let them know the price isn't final until you can come to the house and see for yourself what needs to be done, but you'll probably be able to come close enough for many jobs.
You could also make the initial estimate a little on the high side to weed out some and you can come in lower than your estimate if you want, which will make the customer happy. And if you don't come down off the high estimate the little bit extra helps makeup for those few exception jobs.
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