Modifications:

Worked in the round using this no-purl garter-stitch-in-the-round technique.

The “no-purl” method makes a more visible “seam line” than you would get with knit/purl rounds, and it’s a little fiddly working with the two balls of yarn, but if you really don’t want to purl (or if the finished item will be felted), it’s OK. The second photo shows what the “seam line” looks like.

Rather than try to gather all 80 of the stitches at the top at once, I finished the hat with the following 4 rounds:

1. k2tog around
2. k around (using the no-purl method, or knitting flat - otherwise it would be a purl round) (40 sts)
3. repeat round 1
4. repeat round 2 (20 sts)

Then cut the yarn leaving a long tail, and thread the tail through the remaining stitches and pull tight to close the hole.