Go to
www.mymopar.com and download the 1965 Chrysler FSM. In it, you might discover that the carburetor throttle is run by a cable, that the gearshift has a cable attached to it (possibly as a transition away from the 1964 pushbutton shift control), BUT the kickdown linkage is a solid linkage just as the '66 and later cars have.
Make sure the linkage is hooked up at ALL of its pivots (outside and inside the trans) and is operating. As I recall from the '66 FSM, you put a small rod through the hole in the rear bellcrank support and with the car at hot base idle position, remove the slotted rod and adjust it to just touch the carb throttle stud with the rear of the slotted section, then lengthen it 2 full turns (pre-load), reinstall. From my own experiences, adding another two full turns of preload will raise the shift points such that it will get into 3rd at about 30mph with the 2.76 rear axle ratio at very light throttle. This was suggested to me by an old-line Chrysler service manager, as he'd done it on his '67 Newport and had had no longevity issues with it, which is my experience, too. Raises the part-throttle shift points just enough to make things feel much better and "livelier", too. BUT the key thing is to get the first base adjustment done, first. This was the same man who advised that, related to (factory-set adjustments") band adjustments, "If it's not slipping, don't mess with them", adding that he'd run then "loose" and "tight" with no differences in performance.
Manually shifting the trans, does it act as it should in that mode?
Other than the linkage, internal and external, might check the governor pressures, too. Please keep us posted on your progress.
Just some thoughts,
CBODY67
CBODY67