Trying to ship 8 boxes cross country for a reasonable price (NJ --> CA)

I have 8 boxes totaling 193.6 lbs and they take up about 15.93 cubic feet in space. I've been looking all over the internet for an affordable moving company but so far, the best quote I've gotten is around $671. I was hoping to pay $400 or less. If anyone recommends a moving company, that would be super helpful! I cannot drive cross country so I have to ship the boxes.

Thanks in advance!