I understood about half of what you are saying.
But it is difficult to do verifications according to your rule completely. This is because I have too little experience, skills, knowledge, and time. This means that it is impossible to accurately measure the difference between runs recorded at 60 fps and 30fps. Also, randomizing the start time was your another suggestion, but it is hard too. Who can guarantee that the start time I have determined is random?

I re-measured the HosteL's run and the NutritiousNES's run. Hostel's was 1:06.433 and NutritiousNES's was 1:06.470. There may have been an omission of confirmation in the past records.
The HosteL's run was uploaded via Twitch and recorded using OBS as I don't know how to download Twitch video. And the NutritiousNES's run was downloaded from the following URL (https://ja.savefrom.net/1- (youtube-video-downloader.html ). The resolution is low.
The HosteL's run was previously recorded at 60 fps, but this time I recorded it at 30 fps. I think this method will alleviate the frame rate problem considerably.

Which specific runs are you suspecting?
I use the following rules to verify.
- The video is downloaded locally on third-party service or recorded locally with OBS.
- The counting starts the frame of pushing start-button on 30fps.
- If the video is 60fps, the counting starts modified frame (the really appropriate way to modify it is currently not well understood).
- The counting ends the first frame of exceeding 20k pts.(Same for the other categories)
I have rejudged once the top 3 runs (except HosteL's new run).

For the 20k category in particular, I figure that they are already in a frame-by-frame battle. So recording at a lower frame rate is a bit more advantageous.
Therefore, unifying the start frame independent of fps is an important concern. However, due to differences in recording methods and video submission destinations, I have yet to get a way to successfully unify these. If you have any good ideas, could you please let me know?
Re-measuring all submissions will be difficult for me to do alone, so I will need your help.

I added Switch platform. Switch version is an emulation of NES version.
I don't want you to request adding another platform if you are not going to submit runs on it. Xevious has too many portings. We become not to be able to control this category.

I added WiiUVC platform. WiiUVC version is an emulation of NES version, so WiiUVC version is applied the same rule of NES version.
When the players request, I'm willing to add other platforms. Xevious has many versions on many platforms as far as I know. It is not realistic that we note all of their rules in "Game Rules".
So now we have the policy as I said above.