1998 Cadillac SLS

A bigger battery may not allow it to start any faster, unless the cranking rpms are low. If it cranks normal, but extended, check for a leaking fuel pressure regulator. I am suspicious that you are told the speed sensor is faulty, I have not seen one fail in a decade or so. If the vehicle is driving and shifting fine up to the point that the speedo starts working, it may be an issue with the cluster. If the battery is going dead in a few day, it may have a high parasitic drain that is helping it discharge.