That's a quite an effect, Iacopo! Clearly, dissipative forces don't need large contact areas or long lever arms to generate significant braking torques on spinning tops.
It surprised me when I saw it, because I didn't expect this strong effect.
Then, after some thinking, I considered that, after all, oil has a density and a viscosity that are really much higher than those of air. If air influences the spin time, let's figure out oil. About 60 - 100 mm^2 of surface in contact of oil at the center of the top, (low leverage), reduced the spin time to one third, from 27 to 9 minutes.
Using mm 1 of oil in the base, I guess it would still slow down this top, but much less dramatically, (since only the tip would be in contact with the oil), with spin times of maybe 26 minutes instead of 27. In the past I was used to use about 1/2 to 1 mm of oil in the base. After this test, I became acquainted to use less oil in the base, using often just a thin layer of it.