I do visit NA from time to time, I even happen to have a screenshot from a game yesterday
I don´t think that there´s a huge difference in skill between EU and NA servers, we also got really good/annoying HAs here, you just have to go with the time I guess. I used to play a lot with a lancecav/2h hybrid but that wouldn´t work well anymore nowadays because of all the ranged. Since there´s quite some ranged/throwing/cav going on lately I switched to 1h shield/pole and it amazing how well I can counter them.
If you want to hunt down horsearchers I´m afraid you´ll have to try an archer, xbow or throwing build because HA can only be countered that way. If you still want to stick to a non-cancer melee class, you could try a 1h shield/throwing hybrid. HAs with light horses will have a bad time near you and if they got heavy horses (and if I´m not mistaken), throwing lances count as a pole weapon in melee mode -> instantly stops any cav when you stab it
HAs were one of the main reasons why I made CrossbowBimbo and it´s always damn satisfying when I make a HA fall from his horse and slide into my killhungry team, it´s like throwing a bone into a pack of hungry dogs
tl;dr if you want to efficiently hunt down HAs you have to embrace the cancer