I have not grown Kakai, but I have grown Lady Godiva. If ther is a summer squash plant within a quarter mile, they will cross pollinate giving seeds with hulls. For hulless seeds they need to be completely isolated from all other C. pepo. They are small round yellow squash with vertical black stripes. They definitely don't look like Halloween pumpkins. They are open pollinated compact plants. Usually a squash that is not pollinated will abort at a very tender age, so I am really at a loss as why you have hulls that are empty. It did stay on the vine until it dried , right? If it was picked before it matured, the seeds would not fully mature.

Here is a link that might be useful: kakai pumpkin/squash

My fruit did not match the pix posted by "Kakaigirl". I wonder if mine were not true to type. Wrong shape and wrong color. My fruit looks exactly like a Kubocha.

Yes, I let it fully ripen but not overripen. The "vine" wasn't quite dead yet (probably still isn't) but we had a light radiation frost and it was in November. It had many months to ripen. It was fed liquid fertilizer from time to time and had plenty of water and space around it.

Unfortunately the only reviewer on Dave's Garden posted a description from a catalog and not from personal experience.

Judging from its looks, I would guess that Kukai was bred from Styrian Hull-less. I'll try again with the original, that are described as "strong-growing vines". I am suspicious of the performance of "bush" type winter squash in my northerly climate.

I bought my seed from Bountifulgarden online. A little expensive but worth it just once. Short vine, held up to triple digits, produced two to three fruit per vine weighing from 6-8 lbs. I let them stay on the vine till first frost, then put them in a cool dry area for a month. When my lady friend and I cut them open they were chock full of beautfiul
completely hulless seed. I have not gotten to the bottom of this pumpkins origin. Read all about its history in Styria but nothing from there. Is it some kind of secret, where these pumpkins were bred and by whom? Please let me know your thoughts and together we can find the correct information for curcurbit pepo, var 'Kakai'