Do you have enough cable to make it a "pull to engage" setup? I wouldn't waste more than a few minutes on a rusty push/pull cable- - - -brand new ones aren't that expensive, and one that's long enough to route to the other side of the lever to pull it into engagement will solve the flexing cable sheath problem. Bracketing the cable housing to something rigid like the frame or the transmission housing will also help.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!