You’re so close to conventional, why don’t you set your sights just the slightest bit lower? You only described this house as “close to perfect”. Maybe “sacrifice” just the slightest bit more and not only would qualifying be easier, you’d actually be stretching yourself a little less thin. That said, the present doesn’t seem like the best time to be stretching oneself.
Also, when you say you’re at 50% of your income, are you talking gross or take home? I understand you’re reluctant to share too much detail, but if it should be the former, then no way you should buy this place. In my opinion, of course.