I would really struggle to manage with a 4mm string height, must be really annoying, have you set the relief in the neck correctly using measurement? I had a very high action on my stingray and manage to get it down to just over 2mm using this method:
1: Hold down 1st fret with a capo (or wife or child like i used) and the last fret.
2: Measure the gap between the E string and the 8th fret.
3: I had no gap so had to raise it by turning the truss rod wheel to the left 1/4 of a turn.
4: Measured gap again with feeler gauge at 8th fret trying to get a 0.3mm gap, gap was 0.3 (luck).
5: String height seemed and felt high to me at 2.4mm (the suggested height by most videos on you tube).
6: Adjusted the saddles so the strings were 2mm from the fret-board at the 12th fret.