Palm trees and palm fronds too close to your house are a definite for vermin getting on to your roof and cockroaches live in them and love them, particularly Queen palms.
Most pest control companies do not do mice and rats in attics and if they say they do them, usually do not do them well. It truly is a specialty and usually is not cheap. In addition, it may take a month or two to get rid of them 100%. Madelaine has given you some good thoughts and advice. The main thing, of course, is to find their point of entry. I wouldn't bother doing anything until someone finds that place, otherwise you are kissing your money away on an ongoing basis.
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A Promise Made is a Debt Unpaid
~~ Robert W. Service ~~
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