I have pinpointed to the pixel a vector path drawn with the
pen tool and given a stroke and blending mode; when I use the knife
tool to cut it, there is considerable overlap (2px maybe) that of
course can't be brushed away with the eraser tool because it's not
a bitmap. Any solutions to getting rid of this overlap?
I'm not sure I understand what you mean by overlapping. What
is overlappping what?
There may be a solution, but something else to consider is to
use a mask. You can use a bitmap mask brush away parts of the
vector path as if you were erasing it, but the path remain editable
and you can change the mask later. You can also use a vector mask
which is also editable.