Have you actually verified that by doing as suggested and disconnecting the linkage then moving the shift lever full back? You will not know for sure until you do this.

While the linkage is disconnected, move the lever through the gears and make sure there is a firm detent at each gear, no slop when it's in a detent. There are rare cases where the shift shaft that is swedged into the roostercomb can come loose and cause excessive play.