I was told that for that transmission to operate correctly, there is some linkage related to the carburetor that requires skilled adjustment. Is that correct?
Yes. My daily driver from 1990 until it was T-boned in 2012 was the '57 GMC 102 V8 HydraMatic shown below and I can tell you that both the band adjustments (better done with the pan off using the internal gauge tool) and especially the throttle linkage adjustments (factory gauge is made of un-obtainium) are critical to proper operation of the HM transmission. The specs for the settings of the throttle linkage adjustment is in 64ths of an inch.
I have an original "Hydra-Matic Transmission Operation and Maintenance" Manual for GMC trucks X-5706 (1957) that has a detailed "Diagnosis and Tests" section. If you'd like I could copy that section and post it here.
In the mean time, you could get a feel for non-model specific adjustments by reading through
this manual.
I've also attached FatCo's (probably your best bet for HydraMatic parts) "shift speed chart" which has some basic throttle linkage related trouble shooting hints. The speeds in the chart are probably a bit high for your 3/4 ton truck's rear axle ratio, but you could probably reduce the speeds by 30% or so and be close.
