SPN, the first thing I would do is eliminate the "trailer" style plug especially if doing any kind of a rewire. This will possibly eliminate any weak connections to which these plugs are notorious and pretty much worthless after corroding a bit.
RE the distributor does the centrifugal advance "pop back" when twisted? If so just replace the cap and rotor while being very careful as to the firing order of the wires. A fresh set of plugs (gap @ .040 with the EI) and be sure all connections are clean and well snugged.
As per John do be sure the choke is completely closing!! This is a must for good cold starting.
Check the "spark" and what you want is a spark that is crisp and blue that will pop at least 1/4". This will confirm the coil and the EI.
Dave Neptune