With pump fixed, maybe it sucks the inlet hose so restricting flow when warm?

Hi, just a "heads up"; the grip of the brake drum on the axle can be extremely tight, especially if it was not put on dry of lubricant. From personal experience!

HI Dan'l,
Don't ever be embarrassed when having a lack of knowledge, the ones who should be so are those who are 'willingly ignorant'. 'Ask and you shall receive, seek and you shall find' is the right way.
Now, just a "heads up"; Packard got it right with their ride control design, so try to retain original damping valves etc in your shock absorbers. A "modern ride" is easy to change to, but spoils the "glide" Packard is re-known for.

Just a thought on batteries:
In my 1938 120, I've recently replaced my lead/acid battery.
The 6V 830 CCA lasted ~2 years before a growling slow crank.
The physically larger replacement battery is 6V 800 CCA (cold cranking amps) and is very grunty. Reserve capacity seems to be the key.
I have previously used 800s and they typically gave about 6 years under the same conditions, hence the change back.
My conclusion? It's hard to beat size.
The fit in the battery well is close but ok, though the battery recommended by Packard Motor Co is much smaller.
Weather conditions here are generally 10 to 30 degrees C.

Please remember to protect your lower oil seal by first wrapping the steering box drop arm splines before removing then later replacing it! I assume you have read your workshop manual.

Good things take time. You, not a car, are important.
My 1938 Packard 120 (1602), when I was 23 years old, looked like 18 months work, it took almost 10 years (pre-internet). But it was worth it. Challenge not $$$ build our character.
Good advise from all previous posters. Enjoy!

One cents worth.
The fuel in full carburetor should be enough to go to say 30 mph, so:
1, the off idle transitional jets may be blocked.
Or perhaps an inlet manifold air leak.
2, ignition timing out, test by disconnecting vac retard.

Of course, more sludge = less cooling of the oil !
Unless you have a separate oil conditioner fitted.

Your temperatures sound normal for my 1938 120 (1602) with the optional warmer thermostat (used to improve fuel efficiency/mpg). However, some thermostats have no vent hole to reduce minor boil over or burping of gases, air or localized steam on stopping.
So a solution is to drill a ~1/8" dia hole in the thermostat flange. This I have done with success. Of course if I overfill the radiator it burps!

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HI Fred; can you give us some more info. eg is the motor running evenly as in able to have a coin on edge on its cylinder head? etc. First thought is timing chain.
I like the styling of your car.