As others have noted, something that can be done with a rigid board is not a cool flexible circuit design. And I understand the reluctance to use this for an application that must bend in use when you don’t yet have experience with the way it holds up to repeated flexing, leading to Pete’s suggestion that the right design will use the flex during installation but remain stationary once installed.
One thing that comes to mind is flex versions of SMT breakout boards with the breakout at the head end, several choices of strip lengths, and the corresponding socket for the tail end. Assuming the White Flex Circuits support vias, the flex strips could be double-sided and extremely narrow. This would allow a great deal of leeway in physically routing (low-frequency) signals from e.g. SMT sensor ICs back to control boards in customer projects, something that’s clumsier today using breakout boards and fly wires and bulkier using breakout boards and ribbon cables.