Looking for advice on securing pot/pan rack
I got this rack for hanging pots and pans thinking the studs were at the ends. They are not. Second image shows stud locations in black, wire and pipe locations in red, and blue is where I'd like to secure the rack (however I realized I didn't need to color it all the way down)
I received some offhand advice to simply add 2x4s where I need them and use those. How should I do that?
I've never done drywall anything (except helping hang some one time) so I don't know how best to go about it. I'm willing to learn and have looked up lots of videos. However, cutting into it and then repairing is still a bit daunting.
Should I take out the whole front of the drywall to add 2x4s horizontally or vertically? Or should I make smaller holes on the sides to add the wood? Or is there a better way I'm not seeing.
Extra details:
I have considered a smaller rack but feel it would look a little funny not spanning the length, plus I don't want to.
Behind those studs is the central air intake going up to the higher floor but there is some room back there.
Yes, I did drill through the corner beading already. They sort of hid the studs from my stud finder because they were so much denser than the wood. I later checked again and found the actual studs.