Which speakers did you go for in the end?
True 'White noise' is most likely originate from the source / amplification. Higher sensitivity speakers will naturally amplify any existing level of background noise along with the music.
Also, check if it makes a difference between having the car on or off. It is possible to introduce an alternator driven whine into the speakers if cross-overs are in certain locations - i.e. near the main loom.
ETA - Ignore - didn't see the other responses. Yes, unsurprising to get white noise when adding a full range with tweeter down there! Good luck with your next attempt!