For an unknown reason, even experts struggle with rooting a cutting / piece of saguaro (Carnegia gigantea). I don't know what to tell you other than the usual methods for rooting columnar cactus cuttings don't seem to work and good luck.

Good for you for trying! The honeydew melon one—you’ll want to cut off all rot. As usual, let the ends harden off before putting them in whatever potting mix you use. Keep us posted. I’m interested in these cactuses.

my 2 cents, put them deep enough so they are stable, not “tippy.”

Thanks for your responses. The honeydew melon one rotted in the two weeks I've had it sitting out to callous over - it has turned dark gray/black. It's a separate piece as are the other two. I'm disappointed to hear they are difficult to root but at least now I'll know it wasn't totally me. I gave the largest one to my boyfriend and he planted it about six inches into the ground. I was afraid that might be too deep and it might rot. I'll go ahead and plant mine and say a prayer :)

Just to clarify, when you say "planted into the ground" you mean you are not starting this in a pot?

As you can infer from Alain’s comment, now is not the season, at least in the Northern Hemisphere, to start columnar cuttings in the ground, especially those with low rates of successful rooting.