It seems to me that the Feikert 7" speed test takes into account the effect of the needle on the speed on the LP. So if you're concerned about that, then use this method to adjust the speed!
You would think so, but the Feikert app isn't very accurate. It's designed to measure wow and flutter, but the 7" record is apparently of questionable parentage. There are a number of examples of this app on Halcro's "DD are we living dangerously" thread on Audiogon, and also in Stereophile. In every example the table has a different mean freq. even quartz locked DD models. These tables are more accurate than the app.
There is a DIN record which can be centered and it has a locked groove. This is used with a program and can measure W/F to 0.6% unweighted.
If you want to check absolute speed, I think a laser RPM detector is a better idea, and much less expensive. It will give a continuous readout to a couple of decimal places with the needle in or out of groove. They're designed for high RPM like car engines. Consequently, they're very accurate at low RPM.
neo