Welcome to the Forum.
I am a bit confused and then to the conversion.
The factory brakes on all 1956 Lincolns was 4 wheel drum. The brake booster is called a Treadle Vac system made by Bendix.
You stated, "their is still a small leak in a front caliper on the driver side"
Have the front brakes been converted to disc brakes?
Then you stated, "we are going to buy new front cylinders either way". If the front drivers (LF) side has a caliper where are the cylinders going?
Then you said, "after we bleed the brakes they lose all pressure when the car is running, brake fluid is not leaking like crazy at a stop"
I think this means there is no power assistance and the brake fluid level in the master cylinder does not drop after using the vehicle.
My suggestions -
For the lack of power assistance, you can repair, replace the Treadle Vac booster or have someone do it for you. There are kits that have the seals and other wear items. The shop manual will show how the booster comes apart. And there are a lot of You Tube vids on the matter. Ebay is filled with replacement Treadle Vac boosters from parts only to fully rebuilt with a warranty. Finding one for a Lincoln may be tricky. That booster was used a lot on GM vehicles.
Your stated you are replacing the front cylinders? Why?
I would recommend pulling back the dust boot and inspect to see if there is any wetness. Even slightly would be a leak so go ahead and replace. If totally dry, you are replacing a working part. By that logic taken to an extreme, replace the car. It's working too.
If you feel compelled to replace the Treadle Vac booster and master cylinder, just Google treadle vac. You will find all kinds of replacements. Lots! I am not aware of a kit that has an adapter for the mounting. You will have to fabricate a plate for that. Know that both the plate and modified baking system HAS to be designed to stop three tons of steel. This would not be an area to buy a booster and master cylinder designed for a first gen Cougar. This modification will likely burn up the better part of a $1000 (plus labor) after you get the booster, master cylinder, brake lines and brake valving.
If you do decide to replace the Treadle Vac and you are pitching, I would like the core. I will pay for shipping to Phoenix, AZ 85008.
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