I wonder what the differences are but I guess precision in dimensions or compliance along the belt are factors. A flat belt climbs a crowned pulley to the highest position, and if the belt has the slightest curvature, it will cause small belt oscillation on the crowned pulley. This is due to the physics of the belt-crowned pulley interaction. Another thing is that the inner platter and the pulley axes must be parallel, but that only causes a permanent shift of the belt on the pulley and should not affect oscillating wandering. Another thing that could cause oscillation is that the pulley or inner platter axes are slightly skewed.
Given the results with different belts (3 year old Linn belt, new Linn belt and Thakker belt), it is probably the belt precision that is the root cause to oscillation and the 0.5 Hz harmonics. I've seen other third party belts that I could try, much cheaper than the original Linn belt.