Knitting a fingering weight pattern with DK yarn

Please be kind, I have dyscalculia!

I want to knit the Schene all over fair isle pullover by Kate Davies design in size medium, but the yarn I want to use is DK weight: https://www.ravelry.com/patterns/library/schene

The pattern uses 3.0mm (US 2 1/2) needles to get a gauge of 30sts per 4 inches.

My choice of yarn uses 4.00mm needles with a gauge of 22sts per 4 inches.

I’m an experienced, intermediate level knitter, but I can't for the life of my get my head round how to do this pattern in such a different yarn weight.

To knit this with DK weight yarn, do I need to match this gauge somehow, or should I select a different size garment, or some other third thing? What knitter math/magic is required here?