Whenever a control linkage is involved, ya verify if the desired function works before focusing on linkage adjustments. If the transmission can be shifted into reverse without the linkage, then reconnect the linkage and see what the difference in shifter arms is...the linkage may be bent, changing its motion geometry so that the shifter arm is not functioning properly.
additional information - Fluid Drive setup
The linkage in this Fluid Drive setup has extra steel welded into it, presumably to stiffen this long linkage for better gear engagement.