Just to shed a little light on this, the idea is to increase the weight in EACH of the 6 workouts in a phase. The thing about 5 lb increments is just an example. If you are doing leg presses, 5 lb increments are nothing. The best strategy, especially for smaller bodyparts like arms is to use percentages of the 6th workout, not fixed numbers. I try to stick to 65% or so for the first workout, and go up from there. So your increase on lighter weight exercises may be 2.5 lbs, or 1 lb.
IA, the idea seems fairly sound (I am a HIT devotee myself, just looking for a change of pace). The recommendation is 14-16 sets per whole body workout (my norm is 14 for a 1/2 split workout, so the volume increase isn't a big deal), but working out 3 times a week is new for me (normally twice) so I will be supplementing with 15g of anti-c's (BCAA & Glut) a day to help with recovery.
The biggest problem I see with HST is you don't have a firm handle if you are getting stronger at any point during the 6 weeks, whereas with HIT, I know exactly where I stand at EVERY workout.