The reflective properties of 'normal' glass has mostly to do with the angle it is being viewed from (refraction doing it's part).
I actually do use a very basic interior light source to tone down the reflection of the normal glass in my renders, so your basic idea is sound enough.
The basic glass from the standard template (afaik) uses both the fresnel layer from the transparency channel and the reflectance channel. I think you can turn off the fresnel part by setting fresnel reflectivity to 0%. This means you are left with the Reflectance channel: https://helpcenter.graphisoft.com/user-guide/77474/
this should offer a detailed description on how all the different settings behave.
From your general description, you probably want to have very low 'roughness' and perhaps a 'color' channel to affect the colour of the reflections (maybe something monochrome?).
If it starts to look like something you like, try dialing back up the fresnel reflectivity until you get the desired result for your camera viewpoint. Expect to play with these settings for different camera view points / angles.
I recall a fairly good tutorial to achieve something like this in Artlantis from the ebook that Dwight Atkinson wrote back in 2009, which basically boiled down by 'eyeballing' it by adjusting the refraction until you achieved the (not realistic) artistic look you wanted.
Erwin Edel, Project Lead, Leloup Architecten
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