First, my experience with wildlife management has also been --> no auto insurance company has ever lobbied for increasing deer takes due to car accidents. The cost and payout for deer collisions is rather insignificant when compared to all other payouts. Now other groups have always tried to use auto accident numbers (provided by state farm) to promote their agenda but the data has always spoken for itself. Auto accidents coincided with the amount of motor vehicles on the road or suburban sprawling. Increase the traffic on the roads just so happened to increase deer collisions, go figure, same with reducing deer habitat you then push more deer into the roadsides.
If you believe that auto insurance companies are lobbying your commission then you can find out easily. All meetings are recording and by going over the minutes you will find all public comments and even the subjects being talked about by the commission members themselves. If someone was lobbying then you would find the commissioners speaking about increasing takes at one of these meetings. The same commissioner will also have the data available to support their request for management changes provided by the states biologists. So if you feel insurance is opting for back door deals then you will find a request not supported by the states biologists.
The farmers bureau which represents farmers nearly everywhere is a primary force along with the timber companies that speak about increases in deer takes. Farmers due to crop damage from my experience. This has been pretty universal but also the same reason programs have been opened in most states to allow farmers to harvest deer damaging their crops out of season.