How G fits into this framework.

So starting with my original framework, I worked out how G worked with the space time ratio and that worked.  But then I realized I can express that in terms of Planck mass units that folks are familiar with.  And that works too.  They are the same thing, just expressed in more familar terms at the end.  It is also a more

        m   = m_old * m_scaling
        c   = c_old * l_scaling # m/s

        # space time ratio is invariant at any definition of length
        # s_t/c^3 = 1.35138507828e-43  # has units of s
        # s_t = space_time_ratio* c**3

        # space time ratio is invariant at any definition of mass
        # m/m_P  = 1.35138507828e-43
        # m_P = m / space_time_ratio  #  dimensionless

        # G = s_t/m_P  # from my original common factors framework.
        # G = (space_time_ratio* c**3) / (m / space_time_ratio)
        # G = (space_time_ratio**2 * c**3) / m
        # G = ((m/m_P)**2 * c**3) / m
        # G = m * (1/m_P)**2 * c**3

        G = m * c**3 / m_P**2

There it is.  that is how G is like all these others

        p  = m * c
        h  = m * c**2
        hc = m * c**3

Here is the problem with  unit analysis of a final value when you don't know what values went into a number.  Planck mass only picked up part of the mass that is inside h and G.

G  = m * c^3 / m_P^2

When we isolate the m_P value which scales the mass on the top of the formula with
hc which is hc = m * c^3
So m_P = sqrt ( hc/G) we get the following:

        m_P = sqrt( m * c^3/m * c^3 / m_P^2)
        m_P = sqrt( 1/1 / m_P^2)
        m_P = sqrt( m_P^2)

And when we isolated s_t = sqrt(hcG)

        s_t = sqrt(m * c^3 *  m * c^3 / m_P^2)
        s_t = m * c^3 / m_P

which is just hc/m_P  and if I had recognized that months ago I would have understood things as well as I understand them now. This hidden mass that was cancelled out in the units was hard to see.