I think that "not to want" is preferable because it sounds better, and even accepting that a blanket rule against split infinitives is indefensible (as I do), splitting an infinitive with a negation is uncommon and so sounds wrong.
As for Shakespeare and the split infinitive,
Root pity in thy heart, that when it grows Thy pity may deserve to pitied be (Sonnet 142).
I see this a lot on the boards, and I'm never sure if it's wrong or not. A completely fabricated example would be: 'AIBU to not want to pay for this'. When I read it, the "to not" jars and my mind immediately translates it to 'AIBU not to want to pay for this'. Which is correct, or are both acceptable?
I realise that this is pedantry of the highest degree!