Have you applied appropriate vertical alignment (blue) zones in the font? Your baseline blue zone, for example, should cover both flat and overshoot shapes. Also, check that your BlueScale value setting conforms to recommendations.

Could be because most Adobe apps use a proprietary rasterizing engine…

I've been messing around with the alignment zone settings trying to see if they have any effect. I'll admit the recommendations from John (above) pretty much had my head spinning.

Aside from the basic hinting macro, I am wondering what is the point of dealing with it past that point if Adobe apps are going to do what they want regardless.

Except my font looks ugly in many sizes and resolutions. And it's NOT a particularly ugly font. So I will need to figure something out...

Yes, Adobe uses its own rasteriser, which is why the results may look different between Adobe and MS apps, but both make use of hinting to arrive at those results.

When creating your outlines, did you conform to PS font recommendations regarding nodes at extrema and outline efficiency? Hints interoperate with outline structure, and if you don't have nodes properly arranged the hints won't help and may produce errors.

I usually handle nodes at the extremas carefully. And it is easy to do with broad curves. with smaller shapes, if the extremes start messing with my outlines -- I occasionally ignore them. But not very often and not with this font.

I have been messing around with the blue vertical alignment zones in the hinting layer and futzed with some of the numbers in the additional hinting parameters fields.

Some results were better, some worse. It is a relief to know that Adobe doesn't ignore this stuff completely with it's proprietary rasterizer. I am hoping with a little more experimentation I can dial things in...

Try experimenting with the Blue Scale value (Hinting Settings > Additional Hinting Parameters).
It has quite an effect on the behavior you are describing.