#1
I switch between guitar and bass a lot so I like low action on my bass fret board (especially when I'm trying out jazzy bass solo improvising). I play mainly with fingers.

If I forget about what my right hand is doing while I play something fast or difficult, I start fingering/plucking the strings in towards the body, rather than parallel across the body if that makes sense.

With my low action, the strings (especially E) start going THWAK//THWAK//THWAK, though the notes still ring out properly and it can be EQed out.

Should I
1) Compensate by raising the action (possibly making switching between guitar more awkward).
2) Ignore or EQ it out.
3) Concentrate not to pluck strings in towards fretboard.
#2
I'd just raise the action. You don't want to forget that bass and guitar are two different instruments haha.
ESP Custom Shop 40th Anniversary Eclipse
ESP Standard Eclipse-II
Ibanez AF85VLS
#4
My bass does this too, but I think it's worth it considering the comfort you get while playing. When playing I barely notice it.

So my advice would be to ignore it, and play how you like.