ANSWER - An interesting question - and your enthusiasm and passion make replying to you a pleasure! I always think that the term "witch" is a descriptor of what a person does so to my mind if you are following a craft path and doing what a witch does then terming yourself a witch sounds eminently sensible to me. It's a bit like the old saying - "If it walks like a duck and quacks like a duck then chances are it's a duck..."
So I suppose the key thing for you here is - are you doing the things that a witch does? I'd probably struggle to produce a list of what it is to be a as each witch follows a different path with different priorities and ways of working. What it is to be a witch to one witch may differ wildly to what another might consider the fundamentals of her path. However there are some basic concepts that may serve to generate a broad definition. I'd say a witch usually has a relationship with the natural world, a sense of her own purpose, a belief and understanding in a world that exists outside of the generally accepted and some involvement with magic. There may also be to some degree or another an ability to interact with spirits, the power to heal, psychic foreknowledge or gnosis, knowledge of how to work with herbs and perhaps most commonly and universal among all witches - a sense of feeling out of place in the mundane world.
I'd say from what you write that the term witch would be a fair descriptor of what it is that you do. You speak of your understanding of a world beyond the common place and your talk of the moon and spirits suggests you are focusing on building genuine relationships instead of relying on books for the knowledge that so many mistake for witchcraft (yes books are important but getting out and doing it - that is what really counts.)
You mention magic in the context that you sense it but I wonder if now might be the time to dip the toe in the water and start influencing as well as experiencing. This would be the next step on your journey as far as I can see and the step that will give you the confidence to call yourself a witch and believe it completely. It need be nothing more elaborate than stirring a little goodwill into the evening meal but I think it would be a shame if, being as aware as you are, you didn't take it a step further and put something of yourself back into the world.
I can understand your frustrations with Wicca. I have a good deal of respect for Wiccans and the Wiccan religion but it is not a path that has ever called to me (although I will admit to using its occasional influence in my own work - any trad witch worth her salt "borrows" shamelessly, lol). Wicca can be a little prescriptive and certainly anyone who like yourself isn't drawn to deity worship the focus on the God and Goddess can be distracting. It is important to remember that while Wicca works very well for a lot of people it isn't the only path to witchcraft and if you don't feel it resonates with you then looking for alternative and more traditional ways to practise would be more likely to lead you to your own personal definition of "witch" that will sit more comfortably on your shoulders.
I've never been a fan of titles (or degrees and all that nonsense some Pagans and Witches go in for). To me "witch" isn't a title somebody else bestows on you it is a realisation that you come to yourself when you start to become aware of parts of yourself that stubbornly refuse to make sense in the mundane world. Nobody has the right to say you are or you are not a witch. If you feel the term describes the life you lead, the journey you are taking and the path on which you most feel you belong then it makes perfect sense to refer to yourself as a witch and to embrace that side of yourself to its fullest.
Though if you want my personal opinion I'd say wholeheartedly that you sound like a Traditional Witch!