I'm pretty sure every insurance company has an "appeal" process.
But to answer the real question, we are with AllState. Been with them for lots and lots and lots of years. Like you, we have an umbrella, Absolutely everything we have is insured through them. The few times we've have to use their claims process, they were great to work with. We had a pop-up and the awning flipped over the top and punched a hole in the roof. Insurance paid all but my deductible to replace the entire roof, not just fix the hole. As I remember, the roof was $4000. We only paid $6000 for the entire camper brand new! It was less than 2 years old at the time.
We contacted them again when we had hail damage on our previous Springdale TT. All the vent covers got broken out. We started a claim, but when we found out we could get all of them replaced a local dealer-repair shop close to us could fix them for just a few dollars more than our deductible at the time, we canceled the claim. They they were willing to go that route.
The last time we used the was when I put a dent on the fat fender of my duly. I took the truck to their recommended collision and $0 deductible later (because of vanishing deductible and it was more than 5 years since we've had any claims, and one week, the truck was mine again! Absolutely no hassles, no arguments, no fuss. I think that's why we've stayed with AllState over the years. They may not be the "cheapest" in price, but they do have absolutely great claims service. That's why we stay with them.
And when we had a "flood" in the house, although we have separate flood insurance, the flood insurance is instermental through them, they were great in getting everything we needed and arranging everything. And the insurance ended up pay us an a whopping amount we did not expect, when all we were hoping for was a new carpet. This resulted in an entire remodel of our living family room, which is something we wanted to do for years anyway. It turned out absolutely great!
So, we've used AllState for multiple purposes, including road-side assistance, and they've always pulled through great!