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The spinners shown on youtube clips spinning at very high speeds and for long periods are indeed symmetrical in the rotation axis - often a nest of four or five ball bearing races.
It seems to me that the shape of the spinner probably has the biggest effect on whether the deceleration force is dominated by a linear or quadratic term in speed (assuming comparable balance and friction in the bearing, etc). /snip/ I suspect that there is some sort of kinetic dry friction coefficient effect in the bearing contacts that may explain (or at least model) it.
Both of these hypotheses are testable. BC's photos show he has both an axially symmetric and a lobed spinner whose spin-down data can be contrasted. Also, if a spinner shows a constant drag force term perhaps a tiny drop of very light lubricating oil on the bearings may make that contribution greatly reduced, if it is indeed caused by a dry kinetic friction mechanism.
David Bowman