Keep the Oly 17mm 1.8 or the Panasonic 20mm 1.7?

Does not matter, the 20mm f1.7 in particular is much more sensitive to the issue, and needs to be carefully limited to scenarios where the banding does not show as much.  No other lens I have exhibits this issue anywhere near as badly. No other lens requires me to carefully limit the ISO and only shoot images where there is no large area of shallow gradation.

If it's not the 20mm f1.7, then why do all my other lenses take a monumental effort to show banding, if I can produce it at all?

It's not an easy problem to fix when it pops up either, which means you have to trash a lot of otherwise fine images.

I used to use an old cheap P&S camera that has taken extremely long exposures at higher ISO just fine without any noticeable banding before I got my OM-D & 20mm Lumix combo.  It's really inexcusable.