I can see how much effort you've put into this, it couldn't have been easy.
But I have to say, I feel like the formula isn't comprehensive enough to fully represent the biggest songs in South Korea, I'm gonna try to address a few things.
- You said you didn't include weeks in the top100 of Gaon because that would favor newer songs, but I believe that's a reason to find the correct weight to be given to that criteria as opposed to removing it entirely, following that logic you should remove download certifications because they heavily favor older songs, or you should remove streaming certifications since the favor newer songs. Doing this also puts songs that have great longevity at a disadvantage even against songs released in the same years as them who might've had been a viral hit that quickly fell off.
- If your formula is gonna include downloads and streaming, they need to be contextualized, songs should not be given a specific number of points for X number of downloads/streams without taking into consideration the timeframe in which they got those numbers.
Downloads were impacted by price changes, followed by a trend where people moved over to streaming, on top of that you have key digital platforms no longer making it possible to use.
Streaming grew with time as people moved away from downloads, but even the metric that should be getting the most growth is actually weaker than it should be relative to a few years ago because YT Music's market share kept growing without it being added to Gaon, meaning songs from the past 2 years are getting a bigger chunk of their streams completely ignored and it will get worse with time.
I would say using raw/approximate streaming/download numbers is better than using certification, especially when the gap between each certification is so large.
For example, you can have a song that has the 100M streams and 2.5M DL certifications, compare that to another song that ha 150M streams and 2M DLs, using this formula the first song gets so many more points.
Also 2017/2018 is when downloads and streams were incredibly strong so songs from that era get a huge benefit from this certification based system.