Small, light weight batteries are crazy expensive $200 or so. I can get you the size I have been running, It is an Odysee.
While a failed alternator creates a problem, that is a rare issue. A much lower cost is an ATV, motorcycle type battery for a much lower cost that the light weight "race" batteries. I am thinking about going that route for my next one. Dave Hauck has been using that type here lately.
If you want the exact model that I am using, let me know and I will go all the way out to the garage to look.
Big Dog
PS Get out to the track next month at Thunderhill. I want to see you again, and bring your son.
Jim