>Moreover, the larger the number, the more ways exist to split it into a sum of two other numbers—let alone three.

I don't think that makes sense. Every large odd number has exactly 0 ways to find its sum with two primes^, so they can't have more ways than small numbers (which also have 0, of course). Perhaps he was speaking about the strong conjecture, but then there would be no point to say 'let alone three', because three is only relevant for the weak conjecture.

Am I missing something obvious, or did the author just word that sentence/paragraph poorly?

^I am pretty sure this trivially follows from the fact that two odd numbers always produce an even number.