Any ideas about how to save $$$ on moving costs

If you have a full container, you pretty much pay the going rate for container transport. If you are shipping a 20 foot container rather than a 40 foot container, sometimes the shipper will try to charge you the cost of a 40 foot container anyway, even though they can put someone else's 20 foot container on the same load... and also charge them the full load price.

If you're not being over-charged for the size of container you are sending, your only other hope of getting a discount is to do a lot of research and see if you can find some company that has trucks to send back to Florida empty who would like to pick up even a discounted load to cover some of the cost of the "dead-head" trip.

For people who are not shipping a container and only need to send some pallets of items, you can contact shippers to get rates on "LTL" or "less than load" shipments. The rates vary widely and it pays to shop around. Taking your goods to them for palletizing is much cheaper than having them come to your house to pick up your goods. Trucking companies typically charge per pound and cargo ships usually charge by cubic foot.