You don't have to do the exercises in the exact order shown on the HST site but the two things to keep in mind are: power-lifting/pressing are easier to do when you're fresh and you can perform the exercises in any order you'd like, as long as you do it consistently.
Don't do shoulders/biceps/legs one day and then legs/shoulders/biceps the next. The reasoning is that when you set your max reps you did the workout in a particular order and that means your 'tiredness' is taken into account when you set your max rep. Going back to the shoulders/biceps/legs example, you can see that once you get to legs, after doing shoulders and biceps, you'd have less energy and wouldn't be able to push as hard on legs as you would if you did them at the start of your routine. Basically, changing the order of the exercises mucks the effectiveness of you max reps.
Hope that helps.
As for the strength discrepancy on the last week of 15's, I noticed it too, I don't have a solid explanation for it other than maybe those were weaker muscles?
And finally, on a side note, Harmonized Sales Tax blows and will be the end of tourism (at least in Vancouver).