zerophantom your experience is almost exactly what happened with a friend of mine. She did the manual swiping thing for days and found the profile on day five. And like you said the worst part was not even finding it, it was figuring out what to do with that information after.
I want to add one thing to the swiping method that makes it a little more efficient: use Tinder Web instead of the app. Go to tinder.com on your browser and create the account there. The web version has slightly fewer swipe limits in some regions compared to the mobile app, and it is easier to manage without it being visible on your phone.
Also adjust your distance settings to the smallest radius possible, like 1 to 2 km around where your partner is most often, whether that is home, work, etc. The smaller the radius, the fewer profiles you have to go through, and the faster you might find what you are looking for.
One more thing: if their profile does show up, take a screenshot immediately. Do not just remember it in your head. Tinder profiles can change or be deleted quickly and you want to have that record for when you have the conversation. Not to use it as a weapon, just to have the full picture of what you saw.
Take care of yourselves out there. This stuff is hard 