Based on my general life experience, such as it is, my inherent disdain for how the tort system operates, and the sum total (as a juror) of two civil cases that were "independent" lawyers on behalf of a driver suing someone and their insurance lawyers...
Stick with the insurance company lawyers. They will be sharp, prepared, have lots of experience backing them up at the company office. And they are smart. And dress better.

Insurance companies don't hire fools who fork over the policy limits and then some very often, and when they do, they fire them. By the time the individual has hired a lawyer and discovered he is a fool, it is in the middle of the trial and it is too late. Certainly the company lawyers have the company as their first client, but as long as you are also the company's client, your interests are aligned. If you were doing something that puts you outside your policy coverage, you got problems, but since it just sounds like you "have a choice," I'd stick with the company. It is one of the things you've been paying them for all this time.
In both trials that I sat a juror, it was obvious right off the bat who the "company" lawyers were, even though we weren't told an insurance company was involved. There were two of them, and as I noted above, they dressed well. In the first case, the plaintiff's lawyer was pretty good (and dressed well!) for a lone wolf, but the insurance guys generally played it cool still got a hung jury. In the second, the plaintiff's lawyer looked and acted...desperate. He did a lousy job in court, dumped evidence on us in the jury room that he didn't explain in court, and basically hosed his client. Technically he won, but the judgement was for $300 (three-hundred). His cut of that wouldn't even buy him a new sport jacket, which he desperately needed, and of course did squat for his client.
Grisham writes lots of novels of the poor, underpaid, but noble and savvy street attorney slaying the huge unfeeling corporate goliath attorney, but I'll bet the reality is somewhat different...
Keep us posted and good luck.
edited after I discovered I couldn't spell "desperate".