Solutions to dynamically tune seemingly basic, but important, 'super-parameter'?

I have an algorithm that I'm very content with and am not looking to switch away from the basic model(s) or technology behind them. At the same time I have figured out that the performance of my algorithm can vary wildly depending on the specific values fed to 1 or 2 of what I'll call 'super-variables'. Unfortunately, the solution for me cannot be as simple as just globally choosing the 'best-fit for the most cases', as that is just overly broad for what I'm trying to achieve.

I'm trying not make any assumptions as I try to figure out how to solve this problem but I guess I do have a deep preference for simplicity over complexity even if it costs a little bit in absolute performance metrics. That is to say that I'm very much hoping that there could be a non-machine-learning/AI solution because that would just feel like overkill (e.g., I've gotten this far without those technologies and this seems like detail-level work), but I guess I also have to be open to those options too since I'm currently stuck without a paddle. Please advise.