There's also a lot of demand for moving trucks being used locally as delivery vehicles, since there's a surge in deliveries. Usually not the big trucks, but when a delivery service rents a small truck or van, someone who was going to rent that to move has to rent something bigger.

It's riskier, but you might see if you can buy a used moving truck and plan to sell it at the destination. I've seen a few reports of people doing that with good results, although I can imagine many ways it might go bad.

Or pod style boxes, or load a trailer and a trucking line drops it off at the new place might have better availability.