According to the manual, part #1975 is the correct kick pedal for late 48, J, K, and early L. I believe this is a curved shaft pedal. Part # 1970 is the kick pedal, also curved, for H and early 48 models. I believe the only difference is the width where the pedal rides on the 3/4” shaft. I seem to remember narrowing one to fit on a later bike.
The sector gear and the links are all the same length.
Post some pictures of the mounting shaft. Is it in the same spot as it would be on a model M?
Looking at the above pictures, I think your links are not the same length on the front and back. Any chance the holes in the kicker were redrilled also?