While some of what you say is an interesting thought experiment, I think the second half of this argument has, as you'd put it, a low symbolic coherence and low plausibility.
Recognizing the relevance of coherence and plausibility does not need to imply that other aspects are any less relevant. Redefining truth merely because coherence is important and sometimes misinterpreted is not at all reasonable.
Logically, a falsehood can validly be derived from assumptions when those assumptions are false. That simple reasoning step alone is sufficient to explain how a coherent-looking reasoning chain can result in incorrect conclusions. Also, there are other ways a coherent-looking reasoning chain can fail. What you're saying is just not a convincing argument that we need to redefine what truth is.
For this to be true everyone must be logically on the same page. They must share the same axioms. Everyone must be operating off the same data and must not make mistakes or have bias evaluating it. Otherwise inevitably sometimes people will arrive at conflicting truths.
In reality it’s messy and not possible with 100% certainty to discern falsehoods and truthoods. Our scientific method does a pretty good job. But it’s not perfect.
You can’t retcon reality and say “well retrospectively we know what happened and one side was just wrong”. That’s called history. It’s not useful or practical working definition of truth when trying to evaluate your possible actions (individually, communally, socially, etc) and make a decision in the moment.
I don’t think it’s accurate to say that we want to redefine truth. I think more accurately truth has inconvenient limitations and it’s arguably really nice most of the time to ignore them.