I'm sort of in this boat right now. I wrote an algorithm to solve a problem, and it turns out to be roughly O(n!), which is really terrible, but it works fine in all my test cases because n never gets bigger than 20. Even in real life cases, I doubt n will ever be larger than 40 (which is where it starts to break down).

I'm still going to look for a more efficient way to do it, but sometimes you can go a long way without scaling. Not everything needs to scale to large numbers.