This catagory is called NG+, its basically warpless but on a already completed file. Theres also sub-catagorys. Normal (World 1-8), Special (World 1S - 8S), And All Levels (World 1 - 8S). And also a mario and luigi sub catagory.
Rules: Must start level 1-1 in Big Mario/Luigi Form Time starts when you press a on 1-1 or 1S-1 Time ends on 8-Castle 2 or 8S-Castle Flagpole
Video of a run coming soon
Your description was a category at one point, but no one ran it in the three months it was on the board. There's not enough interest for your idea to be a category.
I plan to request a category extensions page for this game. If it gets approved, your idea could turn into a category. It would probably need more than one person to run it to have a leaderboard, but if you want it to possibly happen I would encourage you to make that video.
@Revelyte23 I did have a video (really a stream), but my internet went out and screwed it up. So it will take a little more time for me to get that video out