My expectation is that ...
636636636 → six hundred thirty-six million, six hundred thirty-six thousand, six hundred thirty-six
636636632 → six hundred thirty-six million, six hundred thirty-six thousand, six hundred thirty-two
636636626 → six hundred thirty-six million, six hundred thirty-six thousand, six hundred twenty-six
636636622 → six hundred thirty-six million, six hundred thirty-six thousand, six hundred twenty-two
636636236 → six hundred thirty-six million, six hundred thirty-six thousand, two hundred thirty-six
All which have ...
$3+7+6+3+7+3+7+6+3+8+3+7+6+3 = 72$ length,
vowel count of $21$, and
digit count of 9,
for LS value of $72/(21+9)=2.4$
are going to be the highest scores.
Each component maximizes the ratio of length to vowels:
"Two" and "six", "twenty" and "thirty" are the highest ratio values usable in their relevant positions. And the longer numbers allow maximum total length of the text for the number.
Other numbers which substitute a "two" for a "six" or a "twenty" for a "thirty", or vice versa, would have equivalent Linguistic Stiffness.