The good news is that scientists are developing a good understanding of what triggers headaches for some people, and it doesn’t seem to be sulfites; all wines contain them. It probably isn’t the alcohol, unless you are prone to migraines or to imbibing too much. The culprit for most people is a class of compounds called biogenic amines, the most familiar of which is histamine. These are not products of the wine itself, but of bacterial contaminants. Fortunately there are fairly quick tests that can be done do measure the levels of biogenic amines, though these aren’t routinely done.
But without testing, the inherent variability of amine production during wine fermentation makes it difficult to predict which wines will be a problem for people susceptible to them. There aren’t any sensory clues, since they tend to have little effect on the taste or smell of the wine. Why there should be a difference between European and domestic wines remains a matter of speculation. Perhaps it relates to the long history of winemaking, with traditional methods naturally sorting out the processes that make drinkable wine and environments naturally free of the offending bacteria. Or maybe it’s just that domestic wines have a higher alcohol content.
In any case, a solution should be achievable now that the cause of the problem is known. It is up to the industry to invest in the technology.