The 'specific heat ratio' is a scientifically concluded exponent value applied to gas behaviour. The 1.2 to 1.4 simply provides a range to cover different conditions/assumptions included in any calculation.
In scientific speak, the 1.2 value is a polytropic value and the 1.4 is a dry air adiabatic value. The known value for air/methanol is apparently 1.3 (approx). The exponent value of 1.3 is also (apparently) highly favoured by individuals that theorise/design.
I did read one argument that stated the value of 1.2 (approx) was probably more relevant, since it served to cancel out other optimistic valve closing calculations etc and provide a more real world figure.
The exponent value chosen does not itself change for different calculations based on different CRs.
It's impossible to know what values Honda used originally. The calculations for engine design may well have been different to real world test results, which would dictate the 'workshop test' figures we see published.
