I find most of my shiny Pokémon during the post-game, so I've never used a playthrough team of all six shiny Pokémon. I may have found/received one shiny during the story mode, but never six!
If the Pokémon Violet DLC counts as a fresh playthrough, I rotated in six new shiny Pokémon to complete the DLC campaigns. It was a struggle, especially against the Blueberry Elite Four.
Teal Mask team: Arbok, Lucario, Chandelure, Shiftry, Lycanroc, and Mamoswine.
Indigo Mask team: Sawsbuck, Scrafty, Kingdra, Golurk, Primarina, and Eelektross.