Suggestions for reliable, affordable moving companies for a cross country move? (South Florida to LA)

I've received a quote from one company, which I have since realized does not include any meaningful insurance in the case of an accident ($0.60 on the pound, which is basically nothing). With full insurance added on + a couple weeks of storage, the total comes out to something like $4,000. For context, I'm moving out of a 750 square foot 1BR apartment so we're not talking a massive amount of stuff.

First, is that reasonable based on experience? Second, are there other companies that are worth getting a quote from?