I am using KP system and some other vedic methods for the btr. I checked the span +/-15 min. of your given time and only the 2 mentioned times were left. After considering the death dates of your parents my conclusion is that you were born at 11.13 pm with Sidereal Asc in Cancer.
Kp astrologers are some kind of passionate about Ruling Planets and I also highly rely on them... If you were born at 13.15pm then your Asc Sublord would be Mars, which however does not appear in the RPs of the btr chart...that's why you can't be born at that time according the Kp rules.