The easiest way to get this carburetor to run correctly is to replace it with the Carter W-1 used by Chevrolet! Oops, that wasn't the question.
The Carter BBR series carbs have a removable (with special tool) idle tube that has a number of very small metering orifices. If these are dirty, virtually impossible to clean other than by removing the tube. Carter suggests that one should never reuse a used tube, but it can be done if one is careful to reform the sealing surfaces.
If you do not wish to remove the tube, you might try careful disassembly of the carburetor, and submergence of the main bowl assembly (which contains the tube) in lacquer thinner for a couple of hours. Remove the body, and (wearing appropriate eye protection and protective clothing) blow compressed air through all of the passage ways that you can see in the idle circuit FROM BOTH DIRECTIONS. This method may work.
On a trivia note: the factory producing the various BBR series carbs for Carter used by Chrysler went on strike in 1947. Carter had sufficient inventory of the carbs to continue to supply DeSoto and Chrysler, but they ran out of Plymouth carbs. Carter then supplied the much more expensive Chevrolet carbs (W-1 574s) to Plymouth at no extra charge, and for a few months in 1947 Plymouth used Chevrolet carbs. This created severe customer service issues in some areas; as the vehicles receiving the Chevrolet carbs performed much better in all respects (power, fuel economy, and driveability) than those with the BBR series carbs.
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Jon.
