For me USAA has always beaten GEICO (and everyone else) for comparable coverage, but I know for others the reverse is true. One thing to consider with USAA is that they typically pay back a dividend on their insurance policies, which reduces the cost of the policies by the value of the dividend.
I would think that the cheapest option would be for you two to combine coverages - by that I mean have one auto policy that covers both drivers and all cars, and also have home/auto/umbrella from the same insurer. That is what I have read anyway.
Personally I try to self insure as much as I can. So if I owned an RV worth $10K and I could be OK if it got totaled, then I'd just not insure it and take the hit if something bad happened. This has the side effect of me being more careful with my stuff, which I think is a good thing.
The same thing might apply to the jewelry policy - if you could afford to pay out of pocket if you lost one of the covered items (like your wedding ring), then maybe consider going without. But you'd both have to be comfortable with taking on that risk.
The thing that I tend to insure for is liability, because I can't afford to pay for damages to other people if that should happen.
Would DH be OK shuffling companies if you did the research and the work of switching?
"At times the world can seem an unfriendly and sinister place, but believe us when we say there is much more good in it than bad. All you have to do is look hard enough, and what might seem to be a series of unfortunate events, may in fact be the first steps of a journey." Violet Baudelaire.