The mistake you are making is confusing angle of attack with attitude.
Angle of attack is angle between the chord line and the relative airflow, not the local horizontal. If the aircraft is heading straight down, the relative airflow is straight up, if heading straight up, the airflow is straight down.
In a glide, the relative airflow is from a small downward angle in front of the aircraft. fly with the chord line at your 4deg to that flow and you have your best L/D. This will NOT be an attitude of 4deg, it would be slightley lower.
Also must say, 60kts could only be speed for best l/d at a particular weight. The actual speed for best L/D will be higher at high weights and lower at low weights.