a local shop that works on classic car restorations. .
I would suggest finding a different shop. Given what they told you, it sounds like they are not as knowledgeable about classic vehicles as they claim.
As the others have noted, the parts are available for the 3 speed, and complete transmissions can be found reasonable. Also, unless the 4 speed is an overdrive version (like the MY6), there is no gain to be made doing that swap. A better choice would be the SM319, which is the same as your existing trans, but with a Borg-Warner R10 overdrive. It's pretty much a direct bolt in.
As far as the rearend goes, unless you have the rare Positraction option (Spicer 45, also used in GMC), parts are readily available for the Eaton H033 differential used in the Chevrolets. The only parts not available are the carrier, axle shafts, and the spider gears. The bearings and seals can be acquired from most parts stores, as well as the crush washer for the pinion gear. Replacement gear sets are axailable, but only in the optional 3.38:1 ratio. The base 3.90:1 and optional 4:10:1 are not.
