However, the main issue with all these compromises is that they don't address the fact that it is actually possible to align a cartridge solely for seven inch records, and by so doing achieve an average tracking distortion of less than 0.1 %.
If you wish to get the best from a 7" record, draw yourself a protractor with nulls at say 56mm and 73mm (which should accommodated singles with inner radius down to 53mm) and use that to align your cartridge.
You will probably find it is impossible with an arm set up for a normal 12"LP unless you can elongate the slots on a standard headshell to reduce overhang, or reduce it by have a sliding base like SME, or with an armboard that can be adjusted by siding or rotating it. The overhang is reduced by around 8.5mm, which pushes the cartridge back towards the connectors.
The offset angle is much reduced also, so would have to be twisted away from the spindle by around 7.5 degrees. The ideal would probably be to use a tonearm with a removable standard headshell, and adapt a spare headshell in order to enable a cartridge to be moved sufficiently.
Even if you are way off with drawing your template by a couple of millimeters in terms of positioning the nulls, it will still give you way better alignment, around 0.1% average distortion, compared with a standard LP set up, provided you align the angle accurately.
Contrast that with average distortion of 0.7% and a max of 2% with the LP set up. With a longer 12" arm, with good alignment you can achieve 0.08% with 0.095% max.
You can see the history in the dimensions. A 78rpm 10" disc has an outside recorded diameter of 9 1/2", which gives a radius of 120.65mm, and an inner diameter of half that, 4 3/4",which gives a radius of 2 3/8" and is the basis of the familiar IEC 60.325mm. A 10" 33.3 rpm LP is the same.
Both 33.3 and 45rpm 7" records have the same nominal recorded inner and outer diameters, namely, 4 1/4" (53.975mm radius) and 6 5/8" (84.1375mm radius), which also isn't such a good match for the 10" alignment, but must also have been an acceptable compromise in the opposite direction to 12" LPs for most record players. I don't know if juke boxes were optimised for 45s. I would hope so
(The above 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 will bring the best out of the records, as the distortion is markedly reduced, and combined with the 45rpm speed, they can sound impressive. Chopping a cheap headshell and using a cheap cartridge would be worth the experiment...
One other point to consider is that using a 12" LP alignment for 7" will need more antiskate than normal, but a 7" alignment will need much less, as the overhang and offset are much reduced, especially if you have a longer arm you can use..