Probably some airlines are more lenient than others.
My experience is that the cheaper airlines are stricter; but that - of course - is extremely variable. Another thing, if I were you, I'd pack it more like a bicycle, I'd make a crate for it, completely enclosed, with a wooden frame inside a cardboard casing. Leaving nothing visible.
You should ask the loading/baggage handlers of potential airlines specifically - don't go through the normal customer service. I'm guessing the best way to get them on the telephone is to call the 'lost baggage' department, who are branched off from the baggage handlers. Ask them questions about how they handle this, and if they scrutinize a sealed cardboard box carefully.
Also, with TSA - they'll open anything. So, if your box gets targeted by them, it's going to be opened and inspected. Luck of the draw. Customs are possibly going to inspect anything international, when you arrive with your 'box' of moped. They have the ability to charge you a duty on whatever you're bringing into the country as well.
If you take the frame only with the fuel tank and carburettor removed, the engine is still going to have a fuel smell to it; you'll be obligated to remove the engine and completely wash it clean, then put it back, anyway. I don't see how your rear dampers are going to be an issue, but if as you are saying, they are an issue - replacements can easily be ordered online.
Just some thoughts. I investigated putting a moped on a train and on a bus, and they have pretty similar restrictions. It seemed like it's possible they could overlook it, that I could 'sneak' a moped into the cargo hold or passenger compartment of a bus or train, but I didn't try it. People do it with bicycles all the time - there's no issue with that, but the issue with the fuel associated with a moped brings it into another category.
Hope this brings a little more perspective into the discussion. Call every airline that flies into Costa Rica and connect with the 'Lost Baggage' department, first of all. They're going to be your best contact, in my opinion.
Good luck with it.
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