There's not much you can do. You've provided a lot of excuses, but no defense. Your vehicles mechanical issues are yours to deal with it. Your red light ticket will also show your speed, length of amber, and how long it was red when you entered the intersection. It's then reviewed by an officer to make sure everything checks out before it's issued. Not much you can do to beat a series of photos.
I wouldn't lose any sleep over it.
Your story would not help you at all getting out of the ticket... you would still be found guilty.
+++ This is not legal advice, only my opinion +++