Re: Pay to take boards to Central America or buy new ones?
Panama = it's notoriously hard to get surfboards. We got asked so many times to sell ours in the water, it wasn't funny. From Dec-April you would have a good chance to find some used boards in Bocas Del Toro (Caribbean Side) but the the Pacific Coast is mainly jungle and the infrastructure is quite bad. I have heard there might be a surfshop in Panama City but don't know for sure. It will cost you at least $400 for a used board though. The chances of finding a traveller just leaving that has a board you like and wants to sell are minimal. I only saw about 20 Western surfers on the Pacific Coast in Panama in 2 months all up and all in Santa Catalina. It's not a crowded place!
Costa Rica now - that is another story - boards galore on every corner - most US visitors ditch their boards on leaving, again it's a matter of luck but with tons of surfers there, you will get a board. The thing is the road up from Panama into Costa Rica goes via Pavones and some other remote places, you would need to get half way up into Costa Rica where most surfers are to get a board.
Other countries and boards: Nica - unavailable, El Salvador - unavailable or old beaters, Mexico - plenty of boards around.
So the short end of the stick is TAKE YOUR BOARDS, especially if you like them, pack them good (let the Indos help you if you are unsure, they are masters at that!) and also take spare leashes/fins/wax and all accessories you might need because you have just been spoiled with the best surf infrastructure on the planet, prepare now to rough it for a while until you get to Costa Rica and Mexico. Enjoy. It's a fun trip with long bus rides in between!