Yes, remove the EDP around the area that you plan to weld. For plug welds, generally 1" diameter.
As far as the weld thru primer, I like 3M Weld Primer II. The II version does not clog as easy as the original. Also, bump the weld current up on notch when welding through the weld thru primer.
When your welds are growing like volcano magma it is because of contamination. Causes are as follows from my experience:
1) Wind from natural causes or even a fan.
2) Rusty metal
3) Oily / dirty metal
4) Primer and Paint
5) Lack of shielding gas (clogged nozzle / low tank pressure)
I always use a tank with 75% argon. I can't go back to flux wire.
I am not a pro welder, but we do quite a bit in the factory and I have done my share on these old cars. If you lived close to KY, I would invite you up and show you what little I do know...