.
That's also interesting that You mention it already has a Ballast Resistor. Normally if You try to start the Car without a Bypass the Ballast gets fried right away. That's why the Bypass from Solenoid was added when 12 Volt System started in 56.

  

Whoever did this conversion did everything as required but left the electrical ground positive with the old starter solenoid. I have no idea why.  The radio has a sticker on it that says it's 12 volt positive ground.  It's DC, can't you just switch the wires on the radio from positive to negative?  After I get the car running with a negative ground, I'll give it a try.  This issue has been fun and I've learned more about old Ford electrical systems than I wanted to know.

That's really strange Phil. Before You switch the Radio I would ask someone who works on these Vintage Radios. There's several listed on the Internet. The fact that its tagged as + ground makes Me think this was not backyard Conversion by someone who didn't know what they were doing. I really wonder if this Car was not exported outside the USA at some Point. Very interesting Car U have.

  

Someone has probably added solid state circuitry to your radio for them to place that label on it. Solid state devices (eg. transistors) can be destroyed by connecting to the wrong polarity. The radio chassis is grounded internally to the radio circuitry, so you can't reverse two wires in this instance.

It is a solid state radio conversion.  It's disconnected for now.  I connected the battery cables with a negative ground, switched out the starter solenoid, ran a new wire to from the "I" terminal and reflashed the existing voltage regulator.  The car fired right up with no issues. Generator is charging.  Problem solved.  Now on to the distributor and carb change.  We are making progress.  Thanks again!

The 57 Distributor went in like butter and the motor fired right up.   The 292 sounds better already.  Don't you love it when that happens! 
What a piece of junk that tea pot carb is.  I don't know why they even call it a 4 barrel?   The thing was leaking gas all over the manifold.  It's in the box now with the Load-A-Matic distributor.  Putting on the '57 intake with new Holley 465 this weekend. 

After I run it around for a few weeks, I'll swap the heads over to the 57 "G" heads with the high ratio rockers and exhaust manifolds.  Funny, the 57 exhaust manifolds don't look much different from the outside.  Should be running like a real Ford soon.

"The thing was leaking gas all over the manifold."
Besides "teapot" they were also known as "the towering inferno"..