Vantz's son, Bill Vantz, has called Post's arguments "laughable."
Post argues his weight, vein access, scar tissue, depression and other medical problems raise the likelihood his executioners would encounter severe problems.
Post's attorneys also want more time to pursue arguments that claims of a full confession by the inmate to several people have been falsely exaggerated.
Post has tried losing weight, but knee and back problems have made it difficult to exercise, according to his court filing.
Post's request for gastric bypass surgery has been denied, he has been encouraged not to walk because he's at risk for falling, and severe depression has contributed to his inability to limit how much he eats, his filing said.
Andrew Welsh-Huggins can be reached at http://twitter.com/awhcolumbus.