Azimuth "recording"

Azimuth

If you can carefully get azimuth correct with each of the 3 cartridges in their own headshell in that arm, then Azimuth is down to the minor movement possible when changing/tightening the headshells.

I use a mirror the thickness of an LP. viewed from the front, is is easy/quick to see a deviation as it is reflected in the mirror. Loosen headshell just enough, a slight bit of movement, tighten.
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VTA: that’s harder, that’s a big reason to have an arm with easy adjustable VTA, with easily marked/found height positions. Any single arm with a scale of some kind you can mark or record, find your previously hard-found preference

This one, sold but up/down is shown well here

https://www.usaudiomart.com/details/649402886-legendary-lustre-gst801/images/1739963/

is absolutely easiest, uses a horizontally rotating lever, easy to put a pencil mark on the base plate.

2nd of mine uses a micrometer to raise/lower the arm, possible to write down height numbers.

http://newartvinyl.ru/board/detali_proigryvatelja/tonarm_black_bird12_5_carbon/7-1-0-41
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VTA: Two arms,

best cartridge in one arm, never change it.

most frequent 2nd cartridge in the second arm, (i.e. stereo/mono arms for instant change during a listening session.

Then put the 3rd cartridge into the second arm that is readily adjusted. Easier: Cartridges with similar desired VTA? Shims to have cartridge body/stylus distance down to lp very similar?

Thanks to help here, I learned about stereo/mono/2 arms. and then I squeezed a 3rd arm on a 2 arm deck, seen in the last photo here:

https://www.ebay.com/itm/133704771410

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.