I don't believe water or [...] have much to do with the extract flavor
I'm of the opinion that, after one masters the "things you want get right when brewing with extract" (see #12), water (both the extract makers water and the home brewers water) matters.
I have brewed the same recipe twice on the same day, changing only the brand of DME (see #3 above). Both were good. Both tasted different. With some of these bottles, I experimented with adding CaCl and/or CaS04 in the glass. Each brand of DME tasted "best" with different amounts of added minerals.
I've suggested an "alternative" model to "water chemistry" in the past.
Water - three parts:
1) initial water quality,
2) adjustment for a good mash,
3) additions for flavor.
With all-grain brewing, see either "
How to Build Your Water" (Bertus Brewing)" or
Brewing Better Beer & Modern Homebrew Recipes. Similar in concept - although one uses "sour malt" the other uses phosphoric acid to adjust mash pH. (Side comment: each also solves the dark grains acidity problem differently).
For extract brewing:
1) distilled water
2) (nothing to mash)
3) season to taste based on the mineral composition in the wort. See #3 for a source of ideas on mineral composition for various brands. Note that you won't get ppm information. But, in my experience, it's a better starting point than what's available for free.
For partial mash brewing, it may be that the approach is:
1) distilled water
2) adjustments for a good mash
3) season to taste based on the mineral composition in the wort.