This can be done. The valves are exactly the same but the adjustment levers work opposite, as you experienced when trying to install.

In addition to swapping the mounting bracket, you will also have to swap the pivoting lever that the cable attaches to. You will have to shave (with a Dremel) the peened over edge of the pivot pin just enough to remove it from the old valve. Then, do the same to the C-body valve and swap the E-body lever in. You can use a pair of vice-grips to clamp back down on the end of the pivot pin to keep it from backing out.

(Take pictures of the old E-body valve to verify orientation of parts)

I did this exact same thing on my car. Same for all E-body and '71-'74 B-body. This is a great way to obtain an NOS factory valve, as long as you have an original to rob the lever from. Hope this helps.