Use some caution in combining quotes extracted from those different pieces of work.

For instance, the one that refers to average temperatures around zero is actually referring to a local area, not the whole planet, and to the average of diurnal peak temperatures, not a 24-hour average!

Also, some of the things you quote are plain wrong.

The orbital eccentricity of Mars is only 0.09, so perihelion is 9% closer than aphelion. With an inverse square radiation law, that gives 18.8% more radiation per unit area, and Stefan's blackbody law gives only 4.4% increase in surface temperatures (neglecting the small greenhouse effect), which is worth about 9.5 Kelvins. Enough to be important, but not as extreme as the quotes you used.

Work on the chaotic variability of Mars spin axis inclination shows that it can vary from a low of ~5 degrees up to a high of 45 or 50 degrees. yes, this does produce strong changes to the planet's climate, and may be responsible for major changes in polecap development, and/or to the layering within each polecap.

However, to think that you can melt significan quantities of water on Mars by these means is pure dreaming, IMHO.

We can discuss this if you wish.