I'm not american and in my country it works just the same way as in England, so I'm just thinking of what could be a reasonable explanation for this difference between a take off and a touch and go.
Maybe the controller considers that when departing behind a heavier traffic from the same intersection, the take off roll will be shorter than the previous one and an earlier turn out would probably help to stay clear of the vortex... Whereas in the touch and go situation, obviously the light one has to land first and then take off , which will use much more runway length and then make it difficult to avoide wake turbulence.
That's all I can think of...
And for your wake vortex on the taxiway, I think it's obviously the vortex from the propellers ... no offense but maybe a tired controller on the position
