Solar Month Count

Yes, along these lines, I used the formula ( with Y = mean year )

mean term-yerm = 1 / [ ( 731 / Y ) - 2 ]

and set this to exactly 24 months. After what mean year could be suitable, I found a 5963 year cycle, but solar months are superior to terms in the realm of this 5963 year cycle. The real cycle is just under half a millenium.
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= 376 yerms
= 753 solar yerms
= 5963 solar months
= 6146 months
= 181495 days
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Composition:
123 15-month lunar yerms
253 17-month lunar yerms
346 nine-month solar yerms
407 seven-month solar yerms
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A Solar Month Count could start just as if an imaginary celestial body, the ghost moon, were reaching conjunction along with the 0th moon of the Brown Lunation Count.

Solar Month Count Zero = JD 2423407.44655 = Brown Lunation Zero

with the months, now solar and lunar
Solar Month Count K  & days ( 1 - 31 )
Brown Lunation  L  & days ( 1 - 30 )