You could always make a new user on your PS4. If that doesn't tickle your fancy though. you could go into Settings -> Application Saved Data Management -> Saved Data in System Storage -> Delete. Hope this helps even though I am two months late!
Could you upload the run on YouTube or someplace (assuming you've recorded it)? I'm interested on how you beat the Infinite Inferno
It would probably be possible but a mod would have to do it and someone would have to do the run but wouldn't it be better to start the timing once you select the diary slot?
There isn't any rule against the game being played on a 3DS but you could use Desmume as long as you don't use cheats. You can record with a camera or with you phone as long as you time it or time it after the run correctly
Mario Kart Tour is a free game for iOS and Android. I think if you go on the Play Store or App Store and just type Mario Kart, you should be able to get it for free
I was wondering if we could use the remastered version for the Switch when it comes out in October. Doubt they would make any changes aside from removing QR Codes since the Switch doesn't have a camera so I'd assume yes.