The best alignment for 7 inch singles?

Downunder

There are no LP alignments ideal for 7" records. Least bad would be Stevenson IEC.

If you wish to get the best from a 7" record, draw yourself a protractor with nulls at say 53mm and 73mm (which should accommodated singles with inner radius down to 50mm) and use that to align your cartridge. You will probably find it is impossible with an arm mounted for a normal LP unless you can elongate the slots on a standard headshell to reduce overhang, or have a sliding base like SME, or can rotate the armboard. The offset angle is much reduced also, so the ideal would be to adapt a headshell to enable twisting the cartridge sufficiently.

Even if you are way off with you template by a couple of millimetres it will still give you way better alignment than a standard set up, provided you align accurately, potentially under 0.1% for a standard 7".
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Downunder,

Interesting that no one has ever designed an alignment for 7 inch singles, or that Loef/Baer ever thought of it.. Given how popular they have been over the years and how manhy squillions have been sold.

Interestingly, all arms at one time would have been designed for 10" records when dimensions were in inches. So when 12" records arrived, they presumably worked acceptably with the existing alignment.

You can see the history in the dimensions. A 78rpm 10" disc has an outside recorded radius of 9 1/2", which is 120.65mm, and an inner of half that, 4 3/4" which is the basis of the familiar IEC 60.325mm.

A 10" LP is the same. (So if you have a Uni DIN which has nulls suitable for a Lof/Baer A alignment with recorded radii at 58.4mm and 129mm that should work well for 10" records.)

Both 33.3 and 45rpm 7" records have the same nominal recorded radii, namely, 4 1/4" (53.975mm) and 6 5/8" (84.1375mm), which isn't such a good match, but must have been an acceptable compromise in the opposite direction. I don't know if juke boxes were optimised for 45s. I would hope so

(The metric conversions are of course unnecessarily precise, and make no practical difference should they be rounded to the nearest millimeter. )

However, using a specific 7" alignment should bring the best out of the records, as the distortion is markedly reduced. Chopping a cheap headshell and using a cheap cartridge would be worth the experiment...

One other point to consider is that using an LP alignment for 7" will need more antiskate, but a 7" alignment will need much less, as the overhang and offset are much reduced, especially if you have a 12" arm you can use.