Pickups are already low. I prefer them that way for some strange reasonWait! You said it's bouncy on the tuner. How close are the pickups to the strings? The magnetic pull from the pickups can cause intonation issues. It's usually seen on the big E string. Drop the pickups down a few turns and see if it will intonate. I've had this happen to me on a Strat before and it drove me bonkers for days. Dropped the bridge pickup down, tried again and it intonated in minutes. Try that before anything else as it's pretty easy to do and reverse if not the cause.