I wouldnt reccomend the 20 rep squats (or even a "hypertrophy block") in your case Raptor, you are constantly having issues with the bar hurting your shoulders/wrists, your knees hurt, etc. A good set of 20 rep squats will likely be very painful regarding your issues and cause you to not complete the sets with adequate loading.
Sets of 5, sets of 6, sets of 3, etc. are going to be more about what you PUT INTO THE REP than how many reps you actually perform. Alot of athletes can focus much better on form, speed, tightness, etc. during a lower rep range and will gain more strength and hypertrophy from this range than they would doing a higher rep set where a high number of reps get sloppy and slow due to different forms of fatigue, irrelevant to your actual goal.
I agree that rotating set/rep ranges is the way to go, I just wouldnt put an exact number on it such as 5 and 8, I would do 4 x 3-5, and 3 x 8-10, or something of that nature. That gives you some room for the days when youre stronger than normal to go up a couple of reps as well as when your not feeling well to still make the rep range.
Its just my personal experience but going into a set "hypertrophy block" for an athlete wanting strength and jumping gains has never worked out well. The switching period is always too long going back to an explosive/speed emphasis and often the CNS is firing on very low levels. But I would never have an athlete do a session that didnt always include some type of explosive strength or reactive type movements in it either. Movement effeciency, cns effeciency, etc. should always be maintained to some degree imo.