I thought about this one some more. Here's the way I'm looking at it.
Let's say we model the load as three single phase nonlinear loads connected in delta. Each of these "wants" to draw a 3rd harmonic current. IF the transformer could supply these third harmonic currents, they would all be in phase with each other (they are 1/3 of a 60-cycle waveform apart which corresponds to 3/3 of a 180 cycle waveform... which is in-phase). However, the transformer secondary, being delta connected is unable to supply these third harmonic currents because of their zero-sequence nature. Therefore the load will create a large 3rd harmonic voltage at the secondary terminals of the transformer as the load "tries" unsuccessfuly to draw it's 3rd harmonic current. With each of the phase-to-phase voltage at the secondary terminals in phase, the total voltage around the delta of the transformer secondary is 3 times that imposed by each single-phase load. This induces a circulating current in the secondary delta. Think of this circulating current as the excitation current drawn in response to a (3rd-harmonic) voltage source hooked to the delta side of the transformer. It will create a 3rd harmonic voltage at the primary wye terminals of the transformer. To the extent that there are loads/sources connected to the transformer primary bus, then third harmonic currents will flow on the primary side (and add up in the primary winding neutral). However, if this transformer is supplied by yet another upstream transformer whose secondary winding is delta, and there are no other loads on the bus, then there would be no path for 3rd harmonic currents in the downstream transformer primary neutral.
So to repeat... my model of the system would be superposition of two voltage sources. The fundamental voltage source is applied at the trasnformer hi-side. The third-harmonic voltage source is applied at the transformer low side. Third harmonic currents flow in the transformer hi-side only if there is some device hooked to the hi-side bus which is capable of drawing zero-sequence (third harmonic) currents. If you have the luxury of lugging in a delta transformer to temorarily supply your transformer, and you can isolate other loads from the bus, I'll bet you neutral currents would disappear (although I'm not suggesting you do this without carefully considering the implications for personnel and equipment safety).
It's worth mentioning that the internal circulating excitation currents on the secondary side may be quite high if the core is going into saturation... affects transformer temperature and load capability.
If you can get a scope, it'd be interesting to look at the primary wye neutral current and the secondary voltage to see how distorted the waveform is.
One question may come to mind in discussing circulating currents within the delta winding... where is the return path for flux? If it is a 5 or 7 leg transformer core, then the flux flows in the unwound legs. In this case the reluctance of the path is low, so exciting inductance is high and excitation current (circulating current) will be fairly low.
However, if this were a 3-leg transformers cores, then the flux would have to travel outside the core to complete the return path. This means high reluctance path, low exciting inductance, high exciting (circulating current).
I believe that core form are generally 3-leg and shell form are 5 or 7 leg. But it's been awhile. Does anyone know?