I have a 62 t-bird COM Medium case behind my 56 292. We did not have all the original parts that went with it so the trans shop that did the work and was very very knowledgeable in these since the owner was in the business since the early 60’s he combined a lot of the 2. He used my flywheel and air cooled torque converter by changing the drive splines to the COM. I would be nice to have the COM out of a 292 pickup with all the correct parts.
To use the original speedo drive gear which went in at the bottom and not the top he machined the tail shaft housing out to take the larger yoke and seal. If he could have found a speedo drive for the COM he would not have done it. The trans he sold me did not have one.. no big deal to me.
The trans is water cooled and I already had the exchanger in a new radiator I had bought. So the trans and converter are double cooled.
The 62 is vacuum controlled so you need a intake line to the modulator. The old throttle pressure arm on the trans is just a kick down non and he put a slotted attachment to my linkage and I’ve adjusted it to only down shift at wide open throttle. Some say you don't need it but I wanted it
I made an extension on the column shift arm to give me an extra spot. He asked if I wanted 2-1-L or D1-D2-L which is called green dot. I chose that because I wanted it. I still need to take off the steering wheel and add about 1/8” to the detent so it will stay in park better. I choose to leave it in neutral with the e brake on. After sitting over a week the converter will bleed down sometimes and fill the governor rear housing but doesn’t leak, I just let it idle a minute and it’s perfect. The only leak I have is it dip stick tube filler at the trans.
The trans swap allowed me to swap the rear to a higher gear where I chose an Explorer 8.8 with 2.74 gear which was perfect for me and what I do with car
Would I do it again, probably not. I’d go to a C4 or GM 200R and change out the gas pedal. Photo of the shift indicator and the extension on the column if you can see it.

56 Vic, B'Ville 200 MPH Club Member, So Cal.