Sounds like lean, Check fuel pump for weak pressure or flow .... ?

The vacuum for the power valve on the model 4000 Holley is independent of the spark advance valve.  The power valve is the brass valve between the main jets in the fuel bowl while the spark advance valve is located on the side of the carburetor.  What carb modification are you referring to?

Are the idle mixture screws responsive?  Screwing them all the way shuts off the engine?  One to one and half turns out on each is normal for a stock camshaft.  Any vacuum leaks will upset the idle and cause the popping noise you mention.

Sounds like you need another  carb.  Shouldn't be that hard to locate another  55 teapot.

I’ll likely just finally install the modern Holley I have put aside, and leave the teapot issue to whatever restorer ends up with my car 😁 (after I check the possibilities that shouldn’t only occur when engine warms, or causes a bubbling sound).
P.S. I wonder, if anyone has filled the market void left when PONY went out of business?  Seems like most current rebuilders lack that same level of tech sophistication.

My quoted post text disappeared (go figure).
Was just curious if anybody has filled the market void left when PONY went out of business?  (Same level of tech sophistication).

CHECK THIS OUT - https://www.hotrodreverend.com/post/1955-ford-holley-4000-rebuild

Also - https://www.carburetor-parts.com/holley-4000-parts

And - https://www.carburetor-blog.com/article-categories/holley-4000/

https://www.carburetor-blog.com/knowledge-base/4000-rebuild/


It all depends on far you want to go with it regarding rebuild/restoration.

Daniel.  Is your particular carb a List #1077 or #1078?  The list numbers will be found at the rear lower flange of the carb.  These two numbers were particular to the 1955 Thunderbird.  Are you looking to simply repair your carb or replace it?  And if replacing it, are you looking for the correct numbered carb for your application or would a non-correct number Holley 4V model 4000 carb be suitable?

Here’s the link to a past thread showing the List numbers of the various model 4000 carbs used by Ford.
http://forums.y-blocksforever.com/FindPost167355.aspx

You post 'anther carburetor'. Do you mean you have a later style carb that you want to install (update) rather than repairing the present 

The cover has several of the air bleeds that control the fuel timing at different RPM. Running without, for other than idle and just off idle, would not work well at all. But as a test after the engine is hot, pull it off to see if it is flooding or boiling fuel.
Ensure your Fire Extinguisher is handy and charged !

Bubbling sounds are usually the gas boiling due to heat soak or lots of air getting in.
Do you have a phenolic carb spacer ? It's 1/2" and black colour under the carb to stop the heat from the intake. Without the spacer the carb WILL get too HOT !
Is your exhaust heat crossover leaking ? that could cause extra flow of hot exhaust into carb area making the fuel boil. I believe the 55 has an intake mounted choke. Was that changed to the later Carb mounted style ?
If the fuel filter has clogged and broken that could let dirt into the needle and seat of the carb making it flood the engine. but that would continue even when the engine cools down.

Just a few thoughts.... :-)

Running great?  This isn't what you said in your opening post..  Seems like you are expecting to much with a carb that seems to have multiple problems.  I have a teapot on my 56, had it rebuild by  professional who specializes in teapots and it runs very well.
As it was mentioned, running very rich can thin out the oil

Another thing that can make bubbling noise is low coolant

It is possible that it is not a carb issue.  A lot of time when things go bad after warming the engine up  up it can be an electrical or mechanical issue.