@TomD8: thank you again. I think it is key that the passage you underline includes the word "total." If instead some part of my income is not part of the other state's resident credit then that part of my income is not precluded from being part of a New York resident credit.
If I have that right then for the original problem, the yet unsolved part is what to do with income, such as bank interest, that is not sourced from a particular state. I am hopeful that that too won't be doubly taxed.
