You have 2 choices both of which came in 52-57 Lincolns and 57 Mercury.. 52-54 used a GM sourced 4 speed Hydramatic. 55-57 used the FOMOCO automatic . Either one would be plenty beefy for your application although both are a bit heavy and bulky. Both should be able to be sourced reasonably priced since it is common for Lincolns that have been updated to more modern drivetrains, with owners selling off the original pieces

Oh and I almost forgot.. In the Super Duty trucks from 57 to 63 you can probably find an Allison heavy duty automatic, which would weigh as much as the engine.

If you need a Hydramatic I can probably help you find one

hello! where are you located! I have some Lincoln parts! 317, 332 truck and 368!

 lincoln/merc. y-blocks &mel's                                                               bucyrus, ohio.