Frank, I have about 42K on a '62 3sp+od so I will be eagerly awaiting the responses on this one. Unfortunately I think you're going to have to pull it and go through the overdrive.
This site may be helpful. Although a Plymouth, the overdrive units are the same as ours.
Several links could be of help here. I have a '69 all-synchro overdrive transmission that I've been threatening to rebuild for 4 years so your challenge may just kick me into gear to finally rebuild the unit. I'm a daily driver year round only vehicle so it would be good 'head insurance' to have the back-up ready to install in the event of a catastrophic failure.
Keep us posted,
Cosmo