God and time. Part of why I think it is no great loss to deny that necessity is real, is precisely because if one tries to say exactly what one means by 'necessary', one will be reduced to saying what you just did, which is that it means 'not possibly', which says nothing if it turns out that 'possibly' just means 'not necessarily'. So, that's part of why I think adding 'necessarily' to 'true' adds nothing whatever and why I can do away with it at no loss at all.
For instance, let's just say that some truths are hoity truths. What are they? Why, a hoity truth is not a toity truth, that's what a hoity truth is. And what is a toity truth? A toity truth is a truth that is not hoity.
Seems to me that in your hands the word 'necessarily' adds no more to 'true' than hoity would. That is, nothing at all. Which if true, means that you agree with me that we can dispense with it, just as we can with hoity and, indeed, toity. Do you? That is, do you agree that both 'necessarily' and 'possibly' add nothing and we can dispense with them and just stick to talking about what's true and what's not? If so, welcome to my view. You are now a guest in the land of the intelligent - don't steal anything.
Now, I do not know what 'possibly' means. I really don't. And I don't think it adds anything to 'true'. However, I can use it to convey to others that I do not believe in necessary truths. And that is how I use it. The English language was developed long before i came here, and by people more ignorant and less dedicated to following reason than I. As such I am fated to have to express myself using the tools of fools. But whatever. If I wish to convey to you that I do not believe in necessary truths - and by extension, do not believe that the law of non-contradiction is a necessary truth - I say that I believe it is contingently true, or possibly true, even though I think 'contingently' adds no more to 'true' than 'necessarily' did.
So, now that you are using English and not squiggles and squoggles, explain to me how my claim that the proposition 'no true proposition is also false' is true - just true, note - generates a contradiction....and do that without popping the word necessarily in