Thanks @oerdnj for insight. For everybody experiencing issues with crappy devices, you should be able to assign different DNS resolvers via DHCP just to specific devices like this:
# cat /etc/config/dhcp
…
config host
option name 'garminwhatever'
option mac '00:12:34:56:78:9a'
option ip '192.168.1.200'
option tag 'googledns'
config tag googledns
list dhcp_option '6,8.8.8.8'