What would perfect technique be exactly?
Do you have to keep your body straight or can you flex your spine and lift your legs a little? I don't use any kipping or swing to gain momentum but I do tend to go into spinal flexion when I max out. I'll even do a hanging leg raise at the end of a really hard final rep. Same thing with weighted chin-ups.
I don't do gtg anymore. I'm using a method from a Ben Bruno article where he says to do 2 max sets 4- 6 days a week. It lets you rest for the rest of the day so you can do other stuff the following day.
Spine could be flexed or extended/arched. Depends on the kind of pull-up. You could keep the lower back with an arch, hooking the feet behind you, and maximally opening your chest (upper back contracted) so your upper body faces more towards the bar. This typically is the "Bodybuilder" way of doing pull-ups, and it makes the pull-up more of a vertical pull -- Row hybrid because of the angle of pull. This is typically used to hit the upper back and even posterior delts harder. When I do them with a lot of tension, I get an unbelievable contraction.
They can also be done in a hollow body shape. That means the spine is flexed, feet are somewhat in front of you so when you pull, your body will be more vertical to the ground. This variation is said to hit the lats a bit more because it's more of a vertical pull. It is also possible to go much higher with this form because your body isn't "stuck" under the bar, as in the previous variation. So this is the preferred choice for Muscle-up work. It'll feel like the bar is a bit more farther away from your body at the top.
It seems a lot of people seem to polarize between the two styles, but there's no reason to hate as they both have merits. You could do most of your strength work with the latter (keeping the abs tight, spine flexed, feet in front of the bar), and throw in the former one for some warm-ups as they're spectacular at warming up the upper back and giving a good pump. Just a thought.
As far as raising your feet in front of you during a rep, it happens because your biceps get fatigued. Raising your feet throws your COM forward, so you can pull all the way up being slightly farther away from the bar. This lets you hit the correct height, without having to fully close the elbow angle. In other words, you're just compensating to keep getting height, through other muscle groups by changing the groove slightly. It isn't
bad in the sense that it leads to worse adaptations. But it
does indicate fatigue. If you're looking to stay fresh on your pull-ups to boost your max, you want to stave off fatigue, so it'd be good to stay away from those reps.
However, the routine you've chosen asks to go for max reps, so in that case, I don't see the big deal with doing the last 1-2 reps this way just to get a few more reps in there.
Hope that helps