We got some red Lily beetle, sounds like a similar life cycle to your invaders. I found stripping the leaves being eaten by larvae and putting them in a sealed bin was one half of the solution. Then when I saw an adult beetle, putting undiluted liquid soap on it was quite effective.
Of course doing that on a dozen Lily plants is a different proposition to a large crop of potatoes, but with some diligence they were gone in just over a week.
It seems if you catch them at the start of their season, it will be much more manageable.