Exit Oni Island
By KTing over the cutscene trigger where Issun turns you back, you can leave Oni Island and go back to North Ryoshima Coast.
When back in North Ryoshima Coast all the triggers that are in place to make sure you go to Oni Island are still there and you can't use the normal Origin Mirror or the Mermaid Spring to warp out. You can however KT up to the Rocky Area to warp out since it was not expected that you could reach there.
Sadly this can't be used in NG+ All Brushes since it would lock you out of getting Gimmick Gear. The third Ida race only starts after you've defeated Ninetails. In NG+ any% this takes too much time since KTing to the loading zone to Kamui takes a solid 2 minutes and overal the strat would only save 12 seconds if you already have the Fog Pot. Getting the Fog Pot ends up making the strat not useful. If you could enter the Kamui loading zone from the top of it, this strat might end up being useful in NG+ any% however.