Spring tension to the left is the reverse gear, that's normal.
Slop can also be the small pins in the top of the housing that engage with the slots in the shifter ball/pivot. Either replace the pins, or try to turn them 90 degrees to where they are not worn.
If that's not all of your problem then last thing could be the shift rails are worn where the lever engages them.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
---All pictures---
"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-