I moved cross country from west coast to east coast back in 2007. It cost me 5k, I should have just sold everything and purchased new when I got here. You are almost forced to buy their insurance or you will find a lot of stuff damaged. In 2018 my daughter was transferred to Florida from Ohio she got quotes that were around 5-7k to move a small 1 bedroom apartment. She sold most of her stuff and what remained was put in a borrowed a 20 foot trailer along with a 1 ton truck from my ex, and I moved her down there myself. The money she saved was significant and went to new furnishings.
I agree that finding a good moving company is like searching for a Unicorn. Think about selling stuff and replacing when you get to your new location and renting a U-Haul. You can hire people to help you load it and unload it and perhaps you can enlist family to drive if you’re not comfortable doing so.