I work with customers that pay out of pocket and also work as an insurance negotiator. I agree with the comment above that I have never heard of a $10,000.00 deductible. Some insurances are basing deductibles on a percentage of the home value, usually 1-1.5%. So I suppose it would make sense if you owned a $1,000,000.00 dollar home.
Here’s what roofing companies don’t want to deal with… We don’t want to deal with someone that has received an insurance settlement, that comes up with a bunch of excuses to not do the work as specified by the insurance, and only wants to replace a few shingles, and have the roof warrantied by the roofing company, and the home owner pocket the difference into their bank accounts. It is possible that the roofing companies in your area are sensitive to that and don’t want part of it. Often insurance companies will write in large portions of the claim as PWI (Paid When Incurred). This means they aren’t going to pay you to do the work unless you actually do it. This makes cash settlements much smaller, even $10,000.00 smaller than cost of replacement. This isn’t a deductible, it ensures that insurance companies are paying for replacement instead of people pocketing cash.
If you have had a storm in your area and insurance companies are paying to have full roofs replaced, roofing companies are going to focus on that work because they make more money for their effort. They are in business to make money so will always focus on where they make the most.
If the damage is as slight as you say it is, you should not need to be in a hurry. Most of the time, slight damage like you describe is not going to cause an immediate leak. Give the roofers in your area some time to replace those roofs that were severally damaged by hail and possibly going to leak due to that damage, and after the work load starts to slow down, they may be more interested in your request to replace “7-8 shingles”. It took almost 3 years for that to happen in my area, but the work will slow down unless another storm hits.