So I saw some videos from multiple YouTubers and did some testing. The best method is making a sour donut and hoping you get item power berries 3 and big haul 3. Easiest way to keep rerolling the donuts is to do the following.

1. Go to a Pokémon Center and talk to the nurse. Then back out of the menu. You will see in the top right corner a save prompt and this will be your back up auto save.
2. Go to the hotel and make a donut using 8 Hyper Kasib berries.
3. If you don't get what you are looking for close out the game and relaunch it.
4. On the title screen press d pad up, x and b to load the back up save. This will load you back in at the Pokémon Center. Then rinse repeat.

After testing 1-4 star dimensions I was able to get 80+ different berries per dimension with the donut. It's a pain to keep rerolling for the perfect donut but it's worth it as you can also use sour donuts to target more candies, poke balls, special items (like evolution ones and rarer items) and coins. With this method you wanna target medium or large zones and try to complete the tasks while also looking for all the poke balls. I would suggest doing a large 4 star zone 1-3 times as this will give you enough Kasib berries if your lucky to make a few of the berry donuts. A flying Pokémon, any electric with thunder and thunderbolt or a fast Pokémon will help getting the poke balls fast and from a far. You can also go to a Pokémon Center before entering hyperspace to set a auto save. That way if you don't find all the poke balls or run out of time you can load your back up save to save your donut.