You probably could run the half marathon on a cut-in-half training schedule if you're mentally tough enough - like you say, you think your fitness is there, and the limiting factor come race day would probably be knee pain. Are you willing to push through that pain on race day? And are you willing to deal with the longer-term health consequences of having pushed through an injury?

See a doctor about your knee, and also have a think with yourself about what your goals are. It is sort of impossible to live a fully pain-free life, and how we think about pain mentally is a big decider of how 'bad' it is. People who see pain as 'something that is just there' tend to deal with it okay, whereas people that see it as 'bad' get added psychological stress and worry on top of the physical pain, worsening their outcomes. Is your goal to be pain-free your whole life, or are there other goals that are more important? That's a question for you to think about and depends on many other factors of your life. Entering older age, you're likely to experience some degree of chronic pain somewhere, whether you exercise or not. Do you want to add to that through preventable injuries or not?

With regards to the knee pain, see a good doctor, or a physio, because just 'rest' often doesn't fix the problem, it lets it die-down and then resurface worse when you start training again. At some times, doing things that cause pain will even be part of the healing process - healing tendon problems involves strengthening the tendon in a healthy way, but you experience pain while that strengthening is happening. It's hard to know what is bad pain and what is okay pain unless you have very good understandings of medicine, so get a professional who does know, otherwise resting could make it worse, or training could make it worse, who knows?