CD head is in Hellraiser 3! I know because I just finished watching it an hour ago. It also features the cenobite woman who constantly smokes cigarettes from her throat, which is very silly.
I think 2 only introduces one(?) cenobite, the elderly doctor. 3 inteoduces 4-5 new cenobites, some of which are really unnecessary.
You’re not wrong that 2 gets goofy, but 3 is where it starts to get brutal.
They even give “pinhead” little quips to say in 3 to make him more like Freddy Krueger. I didn’t hate 3 but it felt like a considerable drop from 2.