How do a secure a wardrobe to a wall if there is a roughly 1.25" gap between the wall and the wardrobe due to the molding on the wall? I'd prefer to not have a screw visibly poking out the back of the wardrobe and going into the wall because it positioned where it will be visible often. Are there any tricks I can employ to avoid the eyesore? Thanks!
You might try something like the Hangman Anti-Tip kits. You can locate the anchors in the middle of the wardrobe so that the hardware isn't easily visible. You would need to hit a stud to really get holding power.
Editing to add that while that would mean cutting a hole through the back panel, this is IKEA furniture, so the back panel is really just cardboard. The anchors for the anti-tip install to the underside of the top, so if this is the route you try, be sure the screws you are using won't poke through the top!