There are many potential sources of slop in the 986 gearshift system. If you have a 5-speed, have you examined your "contraption"? That can be a huge contributor of "side to side slop":
excessive shifter play
This white plastic bellcrank piece is not available as a separate part from Porsche, but is included with new shift console assemblies. It's possible to blueprint the original plastic bellcrank to remove slop, but there are multiple places where it can need tweaking, and it will be some monkey business.
Function first makes a kit that includes an aluminum version of this bellcrank, but it may not be very compatible with your "aftermarket short shifter":
FUNCTION-FIRST > Shift-Right Solution
The factory shifter has a plastic "cage" that surrounds that balljoint, that rides in the slot of this bellcrank. The plastic "cage" spreads out the load from just two contact points out to fairly large, rectangular surfaces:
These are unlikely to wear, and the plastic used has very low friction (especially with a little silicone grease). A potentially major design deficiency of the aftermarket short shift, IMO, is it gets rid of this plastic load-spreading cage and substitutes a larger metal ball in place. Instead of load being transferred over broad areas, it's transferred at specific wear points where the ball makes contact with the planar surfaces.