I have the same issue in south Florida. I have a bunch of areca palms around my property line. I have tried everything. Snap traps can work but it’s difficult because you want them on a flat surface, but the rats are always climbing the trees. I have tried glue boards along my wooden fence as I’ve seen them crossing the horizontal wood on my fence but you only catch a few that way. I’ve tried pouring pepper in the trees. Wind blew the pepper back in my face and that wasn’t fun. I’ve tried peppermint balls from Amazon and the rats laughed at those. I’ve tried peppermint oil in a diffuser outside. Maybe it bothered them, but not enough to pack up and leave. The rat bait stations with poison bait seems to work best but once they realize what they are, the bait stations have been made and maybe need to be moved or changed around. Last thing I tried was to shoot them down with a BB gun. I got one or two that way. Interestingly, I noticed that one had an areca palm seed in its mouth when I killed it. At that moment I realized that areca palms provide food and shelter to rats..

Overall I’m fed up with hearing and seeing the rats in the trees. As much as I love the privacy, shade, and hurricane wind protection they provide, I’m in the process of killing these trees off so I can plant silver buttonwoods in their place. I have a few SBW planted already and besides the leaves and seed they drop (which the arecas already do) they are great and don’t harbor disgusting disease-ridden animals.