I can't quite visualize your cable,

It's just a single-sided, translucent mylar flex cable with 20 "printed"
conductors on 1 mm centers.

but can you cut it at the bad spot, and
clamp it between two pieces of PC board, where one or both PC boards have
traces on them that line up with your conductors? The connection would be
made by compression.

The success of this would depend on how well I could scrape away the
protective layer above the "painted" conductors without removing the
conductive material. I'm not so confident to be able to do that 40 times
reliably such that the resultant bare conductors would all line up nicely
with the PC traces.
--
John English