I'll try to respond to your posting in more detail later, but just to correct something you say about chapter 6.
However, a quick Google will show that the figure usually given is 223 synodic months.
In that chapter, we say that 115 kerbstones is "half the moon swing cycle in synodic months". (P.134).
The moon swing cycle, otherwise known as the standstill cycle, is different to the Saros. The Saros is the cycle which sees the eclipse pattern repeated. There are three cycles: 1. Saros; 2. Moon-swing; 3. Metonic.
So, just to correct, 230 synodic months is the moon-swing cycle, NOT the Saros. If you need further explanation, just ask and I'll help.