Sorry for just-now-git'n-bac, as we had serious health-problems arise w/ our holiday guests ( KIN ) !!!!!!!!!!!!!!!!!
I have not completed enough of the restoration that I can evaluate your shaft-problem, as we intend to replace all-linkages using TEXSOLVE, then test operation before going-on !!!!!!!!!!!!!!!
One might try making one frame ridgid by using 1/2" X 1/16" AL flat-stock across the ends, then checking for improved performance.