That's a good capsulation. One very important thing to remember when making adjustments is that adjusting one aspect can alter the others you have already made, i.e. adjusting zenith can mess up your azimuth. So the proper procedure is to go around the adjustment cycle three or four times to get it all optimized. The RS1500 service manual has a good section on head alignment, describing what each of the many screws on the headblock adjusts. The order they suggest is head height, azimuth, tilt (aka zenith), contact and tangency (aka wrap). After those are done one should check phase alignment.
But before doing any of this one should make sure the tape path adjustments are dialed in. On an RS1500 that can require a lot of little shims that aren't readily available, and it helps to have some good measuring sticks. The RS1500 service manual is pretty vague in this regard, and I am developing a bit more standardized procedure than they offer in the manual for our own tape path alignment procedure. Tension adjustments need to be checked as well and tweaked where necessary. This requires tension gauges and a tenselometer.
You guys know that I am all about DIY when it makes sense. But do consider that it will require spending some money on good test gear and a fair amount of time refining techniques. Taking the tape machine to a well versed tech who has a lot of studio tape machine experience and the proper equipment is probably the best way to get a really thorough alignment.
By the way, Mike Spitz gives an alignment clinic. Naturally he uses an ATR to demonstrate the process and offers a lot of tips specifically germain to the idiosyncracies of that machine. But the general process is covered very well and the class would be a great way to learn how to do it "right".