Eric,
Been playing with this all morning. Added a few twists to your earlier, but essentially came up with a very similar look:
This is the best glass I’ve seen so far in EEVEE. Good work.
Ended up pushing the value really high, and adding a curves node to do finally tweaking for the fresnel. I also created a version which can render flat glass planes. This one needs the Transparent BSDF shader.
I learned a lot by looking at your solution. One thing was the Glass BSDF renders refraction, whereas the Transparent does not.
It appears the backface flag does seem to create some ‘dirty bits’ though I’m not exactly sure why. I understand why you adjust the Trace Precsion and Thickness in EEVEE settings, but even if not adjusted, this glass looks good (though obviously Refraction needs to be turned ON or else it does not work.)
If it’s okay with you, I’ll update my free glass shader and rename it ekRealisticGlass (and link to this thread). That way the 1800+ users who have downloaded it can be notified of the new version.
Thanks again. PS… check out the bottle model: Created with 7 vertices 
https://filedn.com/lLMW4jXsJqxXkRYjd1UCoKL/Blender/ekGlass.blend