I think the amount of offset I'm dealing with is minor. Under a volt DC probably. If the cause is the TVS diode then more likely .7 volts. I think if it's a volt or more it may cause erratic operation on some accessory boards. Electronic e-units, sound boards and the like. I know it falsely turns on my board. The design I use is similar to the DC whistle tender board on the 80's and 90's Lionel tenders. Probably affects those too.
It looks like from Vernon's observation that the later z controllers with the twin MOSFETs are labeled as "Zcontroller" on the front. The older single Triac models are labeled "Z-1000", "Z-500"
I found Vernon's video most enlightening. It clearly shows the mechanism they use for whistle and bell. You can see on the scope that the positive half of the chopped wave expands while the negative stays the same when the horn/whistle button is pushed and vise versa for the bell. That asymmetry is by design, and makes me wonder enough of that asymmetry is what I'm dealing with. I was expecting to see the AC waveform ride up or down on a positive or negative DC value.
The classic Lionel full wave transformers just add a few volts DC to the output and let the AC ride on that to turn the whistle on.