[old man neri]

So during cranking you saw a voltage drop? Perfectly normal. The starter is a huge load, one would expect to see a voltage drop. Think back to years ago, remember seeing cars head lights dim when they were starting their engines at night? Same thing. Your situation might be exacerbated by the age/condition of your battery. Dirty and corroded terminals, grounds, and starter connections could as well.

As for your connector issue I believe that is unrelated to your old battery. It could be as simple as a dirty connector.