Hi Howard,
When our country expert Ann Kuffner found a mover to move her to Belize, she did it online in the USA. Then the mover there coordinated with a broker/mover in Belize. Sterling Freight do international moves and we’ve heard good things about them. Their focus is moves that go via a ship, with the container being brought into Belize City. Their office is actually near San Ignacio. So they may work well for you. Their website is http://www.sterlingfreight.com.
Jason Valdes, of Valdes Global, may be another option. He does moves within Belize, and we’ve found him responsive and very helpful. His e-mail is jkvaldes@yahoo.com.
Hyde Shipping, which is Caribbean Shipping Agency, also has a good reputation. And they do have a decent website here: https://www.hydeshipping.com/3/default.asp?p=home
Hope this helps!