It should be noted that according to US regulations the "export" occurs when someone hands you the item, not when you leave the US. I suppose, though, that leaving with it could require more paperwork. That's one aspect where the "been there, done that" experience you mentioned would be more helpful.
It has been about 6 years since I have been "grilled" on this subject, but as I recall an export is defined as a transfer of material, information, or services between a "US person" and a "foreign person", so the action can require a license even if the stuff does not leave the country. So traveling to the US might not make it any easier to get your hands on what you want. I believe a "US person" does not have to be a citizen, but can be merely a "green card" holder. I don't recall all the specifics there.