Use the side cover and levers from your existing truck transmission and use some longer
bolts with nuts for mounting. Be aware that the 2-3 shift fork is a high wear component and
based on your description of the problems it is likely worn.
You may be able to use one from the car transmission if it is good or pick up a new one.
Disassembly of the side cover is required to change the shift fork. Take a good look at the
gears and other components when you have the cover off. Hopefully the replacement
transmission is better than your current one.
Fred