Sometimes the "Phillips slip" is exacerbated by either the driver or the screw actually being JIS (Japanese Industrial Standard).
https://www.vesseltools.com/handtools/screwdrivers/jis-japanese-industrial-standard
If it has radial core cable housing changing to linear core could help. Another possibility: Your change to smaller crank sprocket may need to lose a link to keep the upper idler from running in to the low gear hub sprocket.