You don't get to infer P from Q which is probably false, and then assert P with conviction.

What if I were to put P = "there is no such thing as absolute simultaneity" and Q = "special relativity"?

Or P = "the earth orbits the sun" and Q = "Newton's theory of gravity"?

As AlephNeil points out, theory unification in physics doesn't invalidate everything that came before; quite the contrary. In the passage from classical to relativistic mechanics, you lose absolute simultaneity but you retain conservation laws. In that case, it may also be said that the feature of classical physics that was retained - conservation principles - was something for which there was ample empirical evidence, whereas the feature which was lost - the existence of absolute time - was an ontological presupposition which proved to be dispensable.

I consider your argument from the supposed incompatibility of QM and GR to be a bad argument precisely because it has no evident connection to the aspect of QM which is at stake here. In other posts, Eliezer advocates for Julian Barbour's approach to quantum gravity. There is a small change in the nature of QM here: in Barbour's theory, there is no time evolution. So the conflict is resolved in a way which does not touch Eliezer's argument in this post.

You also mention string theory as a unification of QM and GR from the particle physics side, implying, I suppose, that it is GR which has been modified. That would be a very debatable assertion. It is a commonplace of the string versus loop debate to present strings as an outgrowth of particle physics culture, and loop quantum gravity as an outgrowth of the culture of gravitational physics (relativists), and to say that the string theorists neglect general covariance (or "background independence" as it is usually termed in such discussions). This appears to be a historical contingency; it is now a common belief in string theory that the real observables all exist only on the boundary, precisely because the bulk has diffeomorphism invariance; and meanwhile, for practical purposes, diffeomorphism invariance is just another symmetry, which you break by gauge-fixing for the purposes of calculation, but which will still be there in the predictions (i.e. the effects of gauge-fixing must disappear by the end of the calculation).

It would be very unusual to argue that the unification of QM and GR requires a change in how we think about particle statistics. If you actually had such an argument, it would be worth hearing, but you don't; you just have an argument which bundles the whole of quantum mechanics into one proposition, and the whole of general relativity into another proposition, an argument which claims that the conjunction of these propositions is a contradiction, and that therefore one or the other is false.

Incidentally, how do you get from that to QM is "very probably false"? "The conjunction of A and B is false" does not imply "A is very probably false"! It seems clear that your problem with QM has nothing to do with the alleged incompatibility with GR - this incompatibility (which perhaps you only believe in because of what various authorities say) merely gives you leverage in debate against quantum dogmatists, or hope for a concrete alternative.

Unless you actually have an argument which makes a connection between particle statistics and quantum gravity, you should just stick to particle statistics, and not bring gravity into the picture.