Not sure what is meant by "High Dollar insurance companies" ...
The companies like Grundy, Hagarty, JC Taylor etc who offer the lowest rates for collector vehicles do have some stipulations in their policies to help lower the risk/exposure -- which they can then turn around to offer lower rates. Up the risk (no lockable covered storage or other than use just for shows and club events, for example) and the rates go higher.
Next up the food chain are companies like Gulfway who don't have as many stipulations but do have correspondingly higher rates.
As always, you have to do your own research to find the lowest rates for *you.* If you can meet the stipulations of the companies with the lowest rates then you get the lowest rate. If you can't (and thus are a riskier policy to underwrite), then you don't get the lowest rates. But you have to do some research to find the companies offering collector vehicle policies to see what their stipulations are.
And also keep in mind that a *lot* of factors go into figuring the policy for each individual. And no two individuals with similar vehicles are probably going to get similar rates from the same company. So say Alvin, Don, Buckshot and I all had the same truck (say a '39 halfton semirestomodded ... just for figgurin'). Based on our driving records, ages, marriage status, education and a number of other factors feeding the algorithms, we might each get our lowest rates from different companies.
Also pay attention to each company's coverages to make sure you are comparing policies/quotes on an equal basis. And know what your state mandates for minimum coverages so you can tell if you are being overinsured. Deductibles ... can you live with a higher one?? If you are a historically good driver, why pay a higher annual rate for something you are likely not going to need? Figure out how high a deductible you can live with and go from there.
But all of the companies mentioned above have good reputations. Some of the regular insurance companies now offer policies for collector vehicles, too, and it might be a savings to bundle that in with your regular car insurance if your particular carrier offers it (like State Farm, for example). Sometimes not.
For example, at one point I had vehicle policies with four different companies: USAA for the DD's, Hagerty for the '49 1-ton and '63 M-37, Gulfway for the '72 GMC road tractor and the '65 fire truck and State Farm for the '01 F-450 farm truck. Since then, Hagerty has expanded its business to cover "retired commercial vehicles" or however they put it. USAA wouldn't cover anything other than regular use modern vehicles. Gulfway wouldn't cover the modern farm/commercial use truck. State Farm would cover all of it but they were more expensive so I elected just to go with them for the farm truck. I let my State Farm agent work up a quote and he even said he couldn't beat what I had put together for myself. But in the process, I had learned a lot about risk, deductibles, minimum coverages and making an honest assessment of my own driving and what would be decent coverage.
If you are willing to put in some time reading and making phone calls and talking to insurance company reps, you can come up with good coverage at a good price.