The two main differences between the beginner and intermediate routine relate to splitting, M/C cycling, and training to failure. The beginner routine serves both as an introductory phase, and, as you correctly surmise, a transition back from layoff. If you had been doing the intermediate routine for more than a few weeks, a one-month layoff does not require you “roll back to the beginner routine” for any longer than two weeks or so. Some people will jump right back into the intermediate or advanced routine, and since I’ve done this myself after a layoff without any problem, I can’t condemn it. I do, however, strongly believe with respect to effort intensity and training to failure, it is better to err on the side of more gradual progression – including gradually progressing back from a layoff. My own experience training others and myself confirms that proceeding methodically and increasing intensity gradually works a lot better than overexerting oneself because of a surge of over-enthusiasm or guilt about taking a layoff. There is no compensating for missed workouts. You just have to make up the lost ground, and move beyond. Fortunately, the detraining effect of a layoff (especially only a month) can be worked-off in just a few workouts. As noted in NHE, occasional layoffs often work to your advantage hormonally, so people shouldn’t feel a need to compensate in any way for missing a few workouts. Over time, however, the significance of consistency and NOT missing workouts largely tells the story of one’s success, assuming he or she is training properly.

Rep range doesn’t matter as much when you’re not training to failure, for reasons discussed in HIE. Higher reps (but not more than fifteen) is appropriate in the beginner routine or when performing warm-up sets at intermediate or advanced level.

HIE contains sample routines applicable to advanced workouts. The most significant change in training regimen occurs between beginner and intermediate. Advanced is fundamentally the same as intermediate, with the addition of numerous techniques you can selectively incorporate into your routine as a means of tailoring training to specific objectives. The added differentiation of the advanced routine makes it more flexible and individualized than beginner or intermediate. For example, you noted three such techniques: overreaching (short-term volume excess), supersetting, and Olympic lifts. Olympic lifts are recommended, optionally, for advanced only and are recommended during the consolidation phase for a maximum of two sets, see HIE p. 212; so they actually are a small component of the program. There’s no supersetting during the consolidation phase so, no, Olympic lifts are never supersetted in HIE program. Follow HIE as closely as possible, but don’t lose sight of the general principles and guidelines which provide you with the framework you need to direct your workouts effectively and constructively.