I would like to share my experience for I have had the same exact problem on my 29 Buick Standard. But the 29 does not have a vacuum tank, after a number phone calls, e-mails etc. these were the consensus of ideas/opinions and this is what I did:
Installed an electric pump.
Cleaned/dissembled/readjusted the carburetor
Installed a new coil.
Readjusted the valves.
As you talk to more people you receive more ideas and become more knowledgeable, good luck