I agree. Your approach is reasonable. Given the stated limits of the theory and variables used for the analysis, the conclusions follow.
You may find this of interest - more later but I've just ran out of available time!
"Greenhouse effect in semi-transparent planetary atmospheres" 2007, Ferenc M. Miskolszi
Abstract—In this work the theoretical relationship between the clear-sky outgoing infrared radiation and the surface upward radiative flux is explored by using a realistic finite semi-transparent atmospheric model. We show that the fundamental relationship between the optical depth and source function contains real boundary condition parameters. We also show that the radiative equilibrium is controlled by a special atmospheric transfer function and requires the continuity of the temperature at the ground surface. The long standing misinterpretation of the classic semi-infinite Eddington solution has been resolved. Compared to the semi-infinite model the finite semi-transparent model predicts much smaller ground surface temperature and a larger surface air temperature. The new equation proves that the classic solution significantly overestimates the sensitivity of greenhouse forcing to optical depth perturbations. In Earth-type atmospheres sustained planetary greenhouse effect with a stable ground surface temperature can only exist at a particular planetary average flux optical depth of 1.841 . Simulation results show that the Earth maintains a controlled greenhouse effect with a global average optical depth kept close to this critical value. The broadband radiative transfer in the clear Martian atmosphere follows different principle resulting in different analytical relationships among the fluxes. Applying the virial theorem to the radiative balance equation we present a coherent picture of the planetary greenhouse effect.
References and background material:
PHYSICS OF THE PLANETARY GREENHOUSE EFFECT
2008 INTERNATIONAL CONFERENCE ON GLOBAL WARMING New York, New York, March 2-4, 2008 PHYSICS OF THE PLANETARY GREENHOUSE EFFECT Dr. Ferenc M. Miskolczi 3 Holston Lane, Hampton, VA 23664, USA, e-mail: f
http://www.heartland.org/bin/media/newyork08/PowerPoint/Tues...
Ferenc M. Miskolczi
Greenhouse effect in semi-transparent planetary atmospheres IDŐJÁRÁS, Quarterly Journal of the Hungarian Meteorological Service, Vol. 111, No. 1, January–March 2007, pp. 1–40 *
Miklós Zágoni, An Introduction into the Greenhouse Theory of Ferenc Miskolczi,
http://hps.elte.hu/zagoni/Miskolczi/hartcode_v01.pdf {LINK not working 2008/12/17.
Ferenc M. Miskolczi and Martin G. Mlynczak
The greenhouse effect and the spectral decomposition of the clear-sky terrestrial radiation IDŐJÁRÁS, Quarterly Journal of the Hungarian Meteorological Service, Vol. 108, No. 4, October–December 2004, pp. 209–251
Ken Gregory
The Saturated Greenhouse Effect June 2008
An introductory review -
http://landshape.org/enm/greenhouse...-planetary-atmospheres-by-miskolczi-a-review/
Discussion
http://heliogenic.blogspot.com/2008/10/miskolczi-climate-model.html
More discussion
http://jennifermarohasy.com/blog/2009/05/the-work-of-ferenc-miskolczi-part-1/
Critical presumption of optical depth
http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=556