It is most likely a wear problem which can't be cured with an adjustment. There can be wear on the rod ends where they connect to the shift levers on the trans. The holes on the shift levers could be also be oversize. You can remove the rods, build up with weld and grind back to size. You could drill out the shift levers and install a bushing or weld them up and re-drill to size. There are bushings for the upper end where the rods connect to the shifter box. They are available from numerous aftermarket suppliers. Once you get the slop out you can make the adjustments.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine