Azimuth "recording"

First of all, you need not be concerned about azimuth  adjustment for a mono cartridge. Since the signal is mono, there is no issue of cross talk. The only thing you should worry about is that the stylus tip sits correctly in the groove. For that I suggest you try for a 90° relationship between the stylus tip and the groove If you cannot actually visualize the stylus tip.. As to the question of setting azimuth for a stereo cartridge, there are two schools of thought. One is to adjust electrically for the least amount of measurable cross talk between the two channels. The other is to forget about that, and set the stylus tip symmetrically into the groove. The downside of electrical azimuth adjustment is that the stylus tip may end up at an angle to the groove walls such that the intended contact patches are not where they should be. This results in both distortion and aberrant stylus wear. After years of adjusting for electrical perfection, I have lately chosen to worry only about seating the stylus tip symmetrically into the grooves. It seems to me the lesser of two evils. 

Hmm, could have sworn the OP said he clearly heard a difference, knows what he wants, and is just looking for a way to mark or reference to be able to easily return to that azimuth when swapping carts. That's it, right?   

I mean, he did say "for quick switching so I can at least eyeball the angle". 

It's hard to say without seeing the arm and how the head shell attaches but what you want is something with one or more reference marks on the head, and one or more reference marks on the arm tube. Simplest/cheapest will be to cut two strips of paper, put some marks on it like every mm, tape one to the head, the other to the arm. Fold and trim so they line up where you want.  

I did something like this on my Conqueror tone arm. It had VTA but no marks to calibrate so no way of replicating different VTA settings. I used a label maker, trimmed the label down real thin, taped it to an acrylic disc, and you can see how great that turned out in my system pics. Look at pics #15-17. https://systems.audiogon.com/systems/8367  I would try something simple like tape and paper first, then if you like it maybe make something better looking/more durable like I did here. 

I absolutely side wide lewm and elliot on this. The most important issues are tracking and record wear. If the cartridge is constructed correctly this will match up perfectly with cross talk results. The mirror trick Elliot mentioned is a great way to make any deviation from vertical obvious. The SmarTractor adds to this by adding a magnifying system which really makes setting azimuth child play. As for being able to quickly repeat the settings, what I think you will need to do is make a protractor for each cartridge. I would use 1/4" plywood. As an example for simplicities sake lets consider a Koetsu which has a perfectly square front. You would set it's azimuth by mirror then take a piece of plywood 3" long and as wide as the Koetsu is high sitting on a record say 3/4". Then you would trim the 3/4" edge to match the angle the front side of the Koetsu makes with the record which ideally should be 90 degrees. You would have to use the protractor gauge you have made with the stylus sitting in the run out groove so your protractor does run over the elevated lip of the record which would change the angle. You would make a label a protractor gauge for each cartridge using what ever surface or angle of the cartridge you can reliably replicate. You could make a protractor for the upper surface of the head shell which is usually flat. 

Gosh. I guess I am not anal enough for this hobby. MC, in my defense, the OP did say something about using the Fozgometer, etc, which indicates he is aiming for electrical perfection, minimizing crosstalk. So I was just describing my own current state of mind, which is that the downside of setting the stylus tip at any angle to the groove walls (for a stereo cartridge), aberrant contact with the groove AND aberrant stylus tip wear, for me is more obnoxious than setting the stylus square in the groove and trusting that the manufacturer did not screw up the positioning of the coils too badly. Yes, the crosstalk data in db may not end up optimal, but the distortions and premature stylus wear associated with the alternative approach are worse. I hasten to add "in my opinion". Plus, speaking to the OP’s actual question, adopting the endpoint of stylus seating in the groove simplifies setting azimuth; in most cases 90 degrees works fine. I probably should have added that point.

@lewm , sure you are:-) But, you have to ignore millercarbon. He always says the same things which means he has nothing to say. 
The OP wants a quick way to set azimuth without marking up his beautiful tonearm. All he has to do is make a few wooden gauges and he is good to go.