Yep you guys are pretty much working toward the right 'way'.
HIIT is all about maximal effort, if your going to do 1minute max periods then its all about going flat out for that minute. If your doing 10 x 1 minute rounds of sprints for example, its highly unlikely round 1-3 will be as fast and hard as rounds 8-10, if they are then you werent going hard enough in the earlier rounds.
Sprinting for 20 minutes or 20 x 1min rounds of HIIT is pretty advanced, especially daily. Most people start with
5mins warm up
5x1 minute sprint period with 1min rest periods
5mins cool down
2-3 times a week, then increase those 1min MAX periods when 5 isnt destroying you anymore.
Im upto 11 rounds now and i am destroyed after it, works wonders for leaning out though and my MMA training in terms of explosiveness.
I should add that theres a few different ways to do interval work, when i measured it, for the 1min MAX period, my heart rate was only really maxxed for 35(ish) seconds, which actually meant i wasent doing the full round effectively.
Now i use a heart rate monitor and when i hit my magic heart rate number, only then do i start counting the 1 minute MAX period.