The code Net::DNS::Resolver->new(nameservers => [qw(1 2 3)]; and the code

@nslist = qw(1 2 3);
Net::DNS::Resolver->new(nameservers => [@nslist];
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are the same, so I think the problem with only the first DNS server being queried is a problem with the Net::DNS::Resolver package or the underlieing library. You might randomize the list of nameservers and reload them in a different order if a request fails.