I avoid using used shifter wires because today's STI levers cause fatigue failure about a half-inch from the cable head, then a strand starts to unwind and shifting deteriorates.
Used shifter housing can be problematic in that it needs to be scrubbed out with a bent-up cable wire, solvent and compressed air, and then may also have an embrittled plastic cover, which serves a structural function.
With traditional brake levers, there's no sharp bends in the system. But the ends of used housings will need to be cut off if sharply bent.
The inner brake wire may break strands at the anchor bolt, especially with older brakes which crimp the cable severely.
Trimmimg the ends of housings fortunately makes the inner wire effectively longer, so the distressed part of the cable can be pulled past the anchor bolt allowing a new portion of the wire to be clamped.
I am less forgiving with cables which show heavy rust, I toss 'em.
Often a "sticky cable" turns out to be either a tight caliper pivot or a coil at the very end of the housing may have intruded into the bore of the housing, interfering with the cable's movement.
Certain lubes are incompatible with the plastic lining in housings, and can create a very creaky actuation. Metallic substances used as extreme-pressure lubricant additives can cause a lot of friction.
I have used current brake cable inner wires as shifting cables, inside of shift housings, for bikes or tandems with very long cable runs, and these worked well as long as I avoided any highly-viscous lube in the housings. The older Campagnolo and other brake wires were even thicker than current brake cable's 1.6mm however.
The OP's problem sounds interesting and I look foreward to hearing the diagnosis.
FWIW, I actually recycle a lot of cables/housings with seemingly excellent results. I prefer the older GripShift "Jonnisnot" lube which is plastic-friendly and effective with a minimal dose applied to the inner wire. I use a PTFE dry aerosol spray in the housings as a cleaner/prep, and as I said I run a bent cable through the housing to provide scrubbing action with this stuff:
