I said "improvise" a noodle, not just try a stock one.

The first step is to find something that fits the stop well enough to maintain a square orientation, so the wire leads out vertically. Typically this would be a stepped ferrule. Then you need to find a way to keep the housing from tugging toward the side, which may be difficult with the limited distance from the stop to seat lug. On some bikes I've solved the issue with a custom bent and fitted stainless steel tube running from the frame stop to the hanger stop. (kind of like a bent car exhaust pipe). Other times, I've used a bent piece of tubing that the housing can slide through to maintain the bend and eliminate the ide tuggijng.

Lastly, I agree that you should scrap the link system and replace it with a traditional yoke and carrier. This will allow shortening the yoke and insuring that the brake is fully applied without the junction hitting the hanger.

BTW- if you can a least find a stepped ferrule, you can address the tugging by using a wire tie and pulling the housing over to the right seatsay so it enters the ferrule squarely. That'll give you something that works right and the time to find a nicer (cosmetically) way to do the job.