Re-reading the orig post, the ONLY similarities to their suggested carb and YOUR carb is that they are both 2bbl carburetors. That's all!!! To me, a "similar carburetor" would be one that bolts right on with no modifications needed, but possibly with some internal items which make it a better option with possibly better design and tech behind it (as an evolutionary situation). Like placing an OEM-spec replacement 4175 where a Rochester qJet used to be . . . just bolt on and works as is.
Now, if that plastic item you reference that makes the engine hard to warm up is connected to the rod that runs the choke plate, might it be the "fast idle cam" that increases idle speed to "fast idle" as the choke plate is closed by the choke thermostat on the intake manifold?
The next concern might be why that item is sticking. Those cams normally "rattle around"| on the shaft they reside on and do NOT stick or bind up, which can be rare.
Additionally, there should be a "choke pull-off" attached to that linkage which will pull the choke open with engine vacuum initially so the engine is not too rich in those initial seconds after trhe engine starts. Is it working, too. holding vacuum?
BUT what also might be happening is that the choke plate is dragging on the carb housing as it closes or tries to open. This is caused by a lont-term-progressing deformation of that carb casting near the air cleaner stud. With time, the tension on that stud from the air cleaner top and the wingnut will pull that area of the carb upward with time. How? From cranking-down on that wingnut to allegedly get a better seal between the air cleaner top and the filter element inside of it. When that warpage happens, it can also compromise the seal of the float bowl's rear divider wall with the air horn of the carb. In some cases, as the choke closes, it can suck raw fuel out of the float bowl and "fog mosquitoes" out the exhaust pipe, at which time, you have to use one foot on the brake and the other on the throttle with the car in gear and trying to drive it, until things get warmed up so that the choke will open as it should. Been there, done that with the Stromberg WWC that was on our '66 Newport 383 2bbl, back in about 1972. One key thing that can preceed all of these things is a drop in fuel mileage as the power valve will be open all of the time, meaning that average mpg can drop several mpg, but run no worse (at that time).
Chrysler did issue a "bridge kit" to address this problen, and it did work well. But that was then and this is now, 40+ years later. Due to the way the air cleaner stud was attached to the prior Carter BBD 1.56" throttle bore 2bbls, they were much more resistant to these issues. AND would be a bolt-in replacement for the Holley 2210 as they were the carb the Holley 2210 replaced. Just go back to about 1969 spplications to find one listed for your engine size.
In the mean time, remove the air cleaner and check to see if there are any shiny spots on the carb air horn where the front of the choke plate might have rubbed on the air horn. IF there is, you might get a small file and dress-down the plate a bit for better clearance (after stuffing a rag into the carb's throttle bores to keep related debris from getting into the carb from this operation). Probably won't take much work, I suspect. Then remove the rag, clean and put things back together, ensuring the complete choke linkage is working as easiily as it can. Some spray carb cleaner on that linkage for good measure, too?
THEN, do an oil change to get the fuel-contaminated oil out of the motor. THEN, do the automotive equivalent of what Davea mentions and get out and drive the car for about an hour on the highway. That will get a bit of the accumulated carbon out of the combustion chambers, too.
This is not the complete fix, but it will explain what's going on and buy you some time to formulate a better solution to your problem than what your operatives are offering you. Meaning a carb that will install without any modifications or extra items needed. Granted, using the Carter BBD 1.56" carb will mean running a different fuel line between the fuel filter and the carb, but that should be it. Be advised, too, that upgrading to a 4bbl can be a good bit more work, fwiw.
PM me if you need to.
Enjoy!
CBODY67