I'd basically agree with your position/argument, but wouldn't totally dismiss (maybe 99% dismiss rather than 100%:) the alternatives. Firstly, regarding ...
How is any philosophical discussion considered viable when it is contradicted by science?
... I'd sharpen "contradicted by science" to "contradicted by observation", where observation means, say, "the reproducible (though maybe only stochastically reproducible) outcome of unambiguous experimental procedures".
But now, even that's arguably debatable re metaphysics. In another post somewhere in this forum, I'd mentioned the ancient Greek epicycle theory of planetary motion. That reproduces observed planetary motion quite, quite well, although its theoretical/metaphysical underpinning that the Sun and (other) planets revolve around the Earth is entirely, entirely wrong.
Indeed, epicycles are in fact a complete set of functions, whereby any curve can be expanded in terms of epicycles upon epicycles, etc. If those Greeks had been somewhat better mathematicians they could've done that, and then said to critics, "Hey, our epicycle results agree with observations to fifteen decimal digits. How could they possibly be wrong???!!! Obviously, the Sun and planets must be revolving around the Earth." So metaphysics must allow for some amount of wiggle room (but maybe not too much) beyond agreement with observations.
Nowadays, for example, we often expand functions in terms of sines and cosines, also complete sets of functions, taking them to be fundamental in some way, and pointing to that same fifteen-decimal-digit-agreement (for quantum electrodynamics where that measurement accuracy is actually possible) as evidence that our theory's correct. Uh, huh. Well, indeed probably so, but leaving that 1% wiggle room might nevertheless be a wise idea.
For example, re general relativity which you cite, there's still no generally-accepted quantum theory of gravity. But what is generally accepted is that when such a theory is formulated, general relativity will just be an approximation to it, accurate in regimes where quantum effects are negligible/ignorable. So how might that more global quantum theory of gravity affect our "metaphysical conception of spacetime" vis-a-vis the conception suggested by relativity? To be determined.
Of course, when predictions of the mathematical formulation of a theory/metaphysical_position are explicitly contradicted by experimental observation, then (as far as I can tell) it's just plain wrong, like you say. But my argument above is that the converse doesn't guarantee "it's just plain right", which I take you to also be implying. (That is, your unsharp word "science", which includes theory, in the above quote maybe implies that. Had you initially sharpened it to "observation", then probably not.)