Have you ever watched videos of cats hunting? Ever notice that the cats are relaxed, even appear dozing, and then suddenly explode into action? Cats are sit and wait predators and are able to go from a more covert monitoring of the surroundings to sudden action extremely quickly. That does make spotting the signs very challenging, but it's supposed to.
As a quick comment: physical punishment is very unlikely to be effective. I used to be of the "squirt bottle" mindset, but it's effectiveness is extremely suspect. Basically, you're assuming that the cat is connecting your aggression properly, rather than seeing it as a reason for their own. In other words, you may be teaching it the exact opposite to what you want to be teaching them here...
Based on various research, cats have a socialization sensitivity period of about 12 weeks and during that period need to be handled and socialized with humans and with other cats. Based on your description, you were handling the kitten from earlier periods, but it was not fully socialized with other cats and that is how it learns some of its interaction skills. In the absence of the other cats, the sole source of learning in this respect has come from your efforts.
Also, as you noted, your cat is skittish, which is another reason I think they problem is insufficient socialization time. Not being especially affectionate is also another sign. The cat is likely to retain this general pattern even if she eventually completely trusts you and your partner. The one thing to be aware of us that a suspicious, distrusting, cat being confined is only going to enhance aggression, not subdue it.
At this point, your better options are to look for ways to encourage the more desirable behaviour and this takes some real patience. When I was much younger, we adopted a persian that had been horribly abused by the "man" (I have a very poor opinion of animal abusers) of the house and as a consequence he was terrified of males and male voices. I spent many, many, hours on my side and stomach talking to him and coaxing him with treats and short pets until he eventually came to trust me and no longer fear. At which point, he became a huge lap cat, one that would happily lie on you and enjoy petting for hours on end.
I think a similar approach may help here. Basically, start out with very short duration pettings and reward her with a treat at the end of the session if she doesn't react aggressively. As time goes by, slowly increase the duration of the sessions, maintaining the reward for success until she overcomes her biting desire. She may never really react to other humans positively, but if you can get her to a place where she will with you, that's something at least. Patience is the key, it can take many months.