Adding an All Secrets category makes sense to me considering the IL All Secrets category. There's a bit of interesting extra movement in the run (and a couple dumb sections where you're jumping down a long rail track for 1m). I think the rules would look like this:

Beat the game. Timing starts once you gain control and ends when you lose control on the last level. The summary screen at the end of each level must display full secrets collected (X of X).

I'm fairly certain that the 1st place Teotl II run on the leaderboard is hacked. I had assumed that the Steam leaderboards for The Ball were reasonably protected, but after looking at the following pages, I'm not certain anymore.

Here is a player who has completed just Pehua and notably does not have the 1500 mummies achievement: https://steamcommunity.com/profiles/76561198029191356/stats/TheBall/ Here is that player at the top of the monsters killed record: https://steamcommunity.com/stats/TheBall/leaderboards/22409

I don't have any reason to doubt times submitted by players such as Living Looney Bin and Dum Dum Dugan, so I'm fine with their scores going into the IL leaderboards. Stimich's Oztoc I and Cahua I-II records are also completely plausible. In the future, it may be best to at least require a screenshot for ILs to be considered.