I thought that "through ticket" probably meant a single e-ticket number, but since it is the most significant issue, thought it important to confirm.
You have this in the right order:
1. Approach SU. It has said "no" and you have that in writing.
2. Approach credit card. Provide them your email to SU, the SU response and a very short & concise explanation of the fact that you were connecting on a single e-ticket and were still charged when SU caused a misconnect. Bear in mind that front like staff who handle these issues do not necessarily understand all of this, thus simple & short is critical.
3. If for some reason, the bank does not end it, then move to MCOL.