" They tell me the big ones fly on board. What to do????"
Hang up flypaper.
Meanwhile, you'd really have to be in a misbegotten excuse for a backwater shack if they didn't have some type of "fumigator" or "bug bomb" available. Hardware store, supermarket, exterminator supply...someone's got to carry them.
Or, if you know anyone stateside, have 'em ship a box of RAID brand fumigators (the smoke bombs, not the aerosols) usually about $15 for a 3-pack. If they get confiscated...not a major financial loss.
And think of something less dramatic than "POISON" to put on the customs' papers.