Since you mentioned the 4x4 routine, I started to experiment with it. I include it in my weekly HIIT schedule, replacing some of the 1-minute by 1-minute routines that I mentioned. I do 3x5-minute intervals separated by 2 minutes of low-intensity recovery. It is a different type of stress, and it keeps my heart rate at max for longer periods than what I achieve with my "standard" routine, even though both need the same time to complete.

To your question: Every 4 days sounds like enough, given your high background volume of high-intensity exercise. You'll probably get a feel for the best frequency, when you sometimes drop to a longer period between the 4x4s. If you feel that your HR gets higher or your stamina drops from previous session to current session, then probably the period in-between should be shortened. But at your level of overall exercise, you also need to be aware of overtraining.