At least staple / thumbtack cardboard to one end of the log and back it up against a wall. It's a temporary solution at best but is budget friendly. I was a half log person until I learned about the Reptile Basics hides and their unique design clicked with my sense of logic. I have been tempted to hot glue cork panels to the outside but have yet to draw up the measurements. Have you looked into Kitedemon's tank flip conversion? It looks like you have the right kind of tank for that.

Mine is a picky winter eater too. I've learned when mine hungry but only because I give her the security of two identical hides (and proper temps.). In other words since all of her conditions are right she must be out and about because she is hunting. She ate yesterday and she ate the 10th but before that it was December something and October before that.