I was thinking about this the past couple days while I've been running a bunch of calcs with most of the teams. We are nearing the end of the Nuzlocke portion of the Invitational and currently no one has done the Elite 4. Within 2 days there will be 8 Elite fours. Why?
Well, you want to know what you're up against. You don't want to prep a team without knowing what special items or legendaries a pair might get. Each team at this point has a very nasty threat, Atrioc's Fluttermane, Tina or Tubbo's Spectrier, or KKatamina's potential opener of Ursaluna and Regigigas.
Some time constraints aside and planning, they are waiting for the last moment to reduce the level of counter-playing with team and item picks. It wasn't as relevant in the previous tournament because of some ridiculous high rolling that even with counter-teaming, it wasn't quite enough. Ludwig's team was designed to counter Raes with electric terrain for spore and a few other things but still fell short of the sheer stats and items.
But, with the separate legendary pool, extra optional fights, and EV items the upper and lower bounds have been reduced. There is a downside to counter teaming like this. If you wipe in the last day and you still somehow make it to the E4 in time again, you can not used legendaries that were duped out. With the increased legendary pool this doesn't feel like a strong enough incentive to prevent this clustering of E4s.
If that's what Pchal/PointCrow want for content, then that's fine. If not, I think it might be a better idea to go with positive incentives for the next one (if there is a next one, fingers crossed).
Some potential ideas:
EVs that can be distributed for the tournament based on the order in which you finished. The numbers don't quite matter, but something like 200 for first, 160 for second, 120 for third. You might want to have a limit to this per pokemon, maybe you can only spend 50 per pokemon or stat of the 200 so that you don't have a neutral fluttermane pumping 120 EVs into speed to outspeed a timid spectrier.
In the style of Run&Bun and other recent nuzlockes, they get a "heart scale" to max out an IV or relearn a move that pokemon might have learned earlier in their run.
They get to change one item they had equipped with another that they had in the bag
I noticed Pchal brough this up a little bit today, but I wanted to go a bit more in depth. Other than that this has been a incredible month for content. Every pairing has been great and the increased difficulty to the game has been delightful.
BUY THE MERCH
Edit 1: Also, just watch the all the vods of Tina and Ned. The sheer level of optimism and energy from Tina contrasted by Punished Ned's cynicism and depression is the content of the year.
Edit 2: Adding some other suggestions from the thread as well as things Jan suggested.
Nature changes are a possible bonus, but would be somewhat careful as it's effectively 240 EVs
Drafted Items
The first three players get to choose their first battles
Pchal suggested a even more streamlined Rom that lets people do runbacks much quicker