But that's not how to say what you want to say. Every true proposition is a true proposition, but not every true proposition must be a true proposition. Is, yes; must, no. Not every truth is a necessary truth, for some truths are contingent truths. Only propositions that must be true are necessary truths.
The proposition "the cat is on the mat" is true, but it's not so that it had to be that way, so that it is that way isn't to say it must be, and if it's not the case that it must be, then it's a contingent truth, and if it's a contingent truth, then it's not a necessary truth. So, although the proposition is true, that's not to say it must be true.
You are using "must" in a way that I used to use "must" before I learned not to. If you flip a quarter (that is heads on one side and tails on the other), and if it lands on one or the other, then if you know it didn't land on heads, then you think it must have landed on tails because no other option was available, but it was never the case that you had to flip the quarter, so although it landed on tails, it's not the case that it must have landed on tails --because things could have turned out differently such as you never even flipping the quarter. You should be very cautious not to declare a truth a necessary truth just because something is the way it is.
You keep returning to an inverted view of necessity, so let me put it in an way that shows it. When you say that "every truth must be true," you must remember that:
A truth is whatever is true insofar as it is true.
Being true is being the same as whatever makes what is true a truth.
Hence, the sentence "every truth must be true" informs us that whatever is true must be the same as whatever makes it a truth (some white snow must be the same as the whiteness of some snow, otherwise it ceases to be a truth). You could rather say that every truth depends
on its truth - a true being - without fundamentally altering the meaning of this necessity. The necessary truth of any truth refers to the true being that gives truth to any truth rather than to the truth being true: it does not refer to the truth in your head: it refers to the truth outside your head, which makes the truth in your head true. It is the truth outside your head that is necessary - necessary for the truth inside your head to be true - not the other way around. It is in this sense that every truth must
be true, and only this reading makes any sense out of, "if any truth were untrue, then it would not be a truth: every truth must be true." If you read this the way you were reading it, then you get:
If any truth (a true being) were untrue, then it would not be a truth (either outside or inside my head): every truth (a true being) must be true (first as a being in the world, and then as a truth in my soul).
Which is the modal fallacy. This reading is wrong simply because it puts an ideal truth exclusively outside of me, confusing a truth with the true being that gives it its truth. Now, if you read it the other way around, then you get:
If any truth (in my head) were untrue (as a true being in the world), then it would not be a truth (inside my head): every truth (in my soul) must be true (as a being in the world).
Now there is no fallacy, and you can see the two different truths, despite their identity: a truth in my head must be true outside my head, otherwise it is false.