Marvel, sorry so late in getting back to you..just got back from paradise!
I think you might have misunderstood my post. You bring the meat with you, you don't pick it up there. The permit allows you to bring in USDA meat that you have bought in the USA.
This said, the permit only cost $5US and there was no duty (this time anyway...you never know!)
When you arrive in Belize City, you go to the "Goods to Declare" line after going thru immigration. There you tell them about your meat, show the meat and the permit to the quarantine officer, pay the $5 for the permit...and off you go!