I will grant you that if you do an experiment at high energy, but well below the Planck energy, and see such resonances, then yes, you'd have evidence for strings. Except... you might not see those things, and failing to see them doesn't invalidate the theory.
The models that predict these are based in perturbative string theory, no? That's explicitly an approximation, and to my understanding it is not at all clear that you expect that behavior in reality (which, as far as we can tell, is not perturbative). Last I read, M-Theory, in general, does not require such resonances. And there's a bazillion ways to collapse the multiple dimensions required by string theory down into 3d models that give particular predictions of what resonances you see - so, if you run an experiment, and it fails to show the resonances, you just say, "Well, I have the wrong perturbative series/compactification, but string theory hasn't been disproven!"
While I will grant that we don't know the final high-energy description of M-theory yet and can't give a quantitative prediction, the expectation would be to have membrane resonances there. As for the perturbative/nonperturbative issue, one of the neat/amazing things about the framework of string theory is that almost every point in parameter space, even if it looks naively nonperturbative, can be mapped to another description where perturbation theory works pretty well. (Remember that the coupling constant doesn't actually have to be that small for perturbation theory to be ok.) So you would generically (in the technical sense) see stringy/membrany resonances with some width. They'd only mush out and become indistinguishable (and get pushed right up to the Planck scale) in an unusual area of parameter space. So, say you don't see the resonances. Then,
just as in every other theory/model, you can put limits on parameters. This is worth emphasizing. If I have
any proposed theory, there is some kind of free parameter(s) to fit to experiment, and your prediction depends on those parameters. So
the totally normal case of "falsifiability" means being able to put limits on free parameters. It's only when you have some way to
measure parameters and then make an additional measurement that you can make a
quantitative and possibly unique prediction. String theory is no different than any other theory in that way. Now, by the time we can build a Planck-scale (or even a bit below) accelerator, it's quite possible we could measure various parameters of string theory with cosmological measurements (or, more precisely, say what the parameters would be if string theory correctly describes cosmology), which would allow quantitative predictions for the collider results. Again, falsifiable like anything else.
And, if you do somehow manage to run a test up a Planck energies, you still have an issue - more conventional theory also predicts that you will see some really strange things there (like black hole states), so you can't tell if what you are seeing is string theory, or something else.
Again, generically, the string resonances should be lower-energy than black holes. And, of course, to understand quantum black holes in a particle collider, you need some kind of quantum gravity theory, none of which are conventional field theories. In more general situations, yes, it is generally possible to cook up a quantum field theory that does basically anything that string theory or any other CPT-preserving unitary theory can do. But that may require a lot of epicycles. At what point do you allow Occam's razor?
Thus, the whole thing leans to the non-falsifiable. If you can always dodge and say that your theory is still correct, there's an issue.
Let me ask a rhetorical question. Do you think quantum field theory is falsifiable? I can certainly falsify specific quantum field theories, but within the framework of QFT, it's possible to get many many different results and/or avoid all kinds of limits. It's a similar situation with string theory --- there are many possibilities overall, but a given set-up can be ruled out or limited as normal.
Meanwhile, the most recent stuff I saw on quark-gluon plasmas coming our of the LHC *failed* to match the string models used to describe them. And no SUSY, though that should have been seen in Bs decay.
We need to be careful here. We've so far been talking about string theory as a "theory of everything" (or ultimate description of the universe). With the quark-gluon plasma issue, you're now talking about string theory as a dual description of nuclear physics, meaning it's a way to calculate in a theory (quantum chromodynamics) where calculations by usual means are prohibitively difficult. In that case, it would have been a big surprise to see quantitative agreement between the string models and the experiment, because the precise string models used are not supposed to describe real-world QCD closely but rather similar theories which are a bit easier to work with. The lesson here is that QCD is hard, and we have a way to go with both traditional methods and dual string theories. It's worth noting that the first qualitative understanding of quark-gluon plasma results from RHIC was due to a dual string theory model.
As for supersymmetry, you're again talking about limits on parameter space. Yes, there are now strong limits on the minimal version of SUSY, though it's not nearly closed off yet (I'd warn against articles in the popular press about that, though, since the "SUSY is ruled out" soundbite sounds so good despite being inaccurate according to community consensus). On the other hand, the Standard Model is a far-from-minimal extension of the subatomic physics we knew 100 years ago, so it's maybe not so surprising if low-energy supersymmetry turns out to be non-minimal.
Back in the 1980s, Feynman stated concerns that there was rather too much hype and groupthink surrounding string theory, and I don't see a lot of evidence that's gone away. How many times does a model we've been trying to develop for 40 years have to fail to meet expectations before we collectively stop apologizing for it? So, as you say above - yes, I think it fair to say that at this point string theory is over-represented, and we should start putting more legitimacy on other avenues of thought. While there may be some people here or there working on other things, it seems to me that the community as a whole really has all the eggs in one basket.
Interestingly, I used to work at CalTech, where of course Feynman spent a large part of career, and so has John Schwarz, known as "the father of string theory" (and, at least until his recent retirement, the resident of Feynman's old office). From what Schwarz and others who were there with Feynman have told me, Feynman was not so negative about string theory in general as his famous quote would lead you to believe and was in fact supportive of Schwarz's work, at least.
Anyway, I'm starting to feel like we're just getting into a back-and-forth (and rather away from the OP's topic) between just the two of us, so I'll leave with a last couple of thoughts unless other posters ask for more information:
1) It's certainly fair to have an opinion that string theory is over-represented. It's an opinion. I'd note that there are actually quite a few people working in different areas of quantum gravity. Though they are not as unified in what they're working on, I wouldn't classify it as "all the eggs in one basket." Anyway, it's also fair to note that there is sometimes overlap between different approaches (including string theory) and that all approaches to quantum gravity face the same fundamental obstacle in making predictions --- they have to extrapolate over about 16 orders of magnitude in energy. If you think quantum gravity is worth understanding, it's going to take time, no matter what approach you favor.
2) If it seems like string theorists have been "apologizing" a lot, it's because a relatively small handful of physicists decided to attack it in the popular press. There isn't a need to apologize --- string theory has actually been remarkably productive whether or not it is an ultimate theory of everything. I don't have time to type it all out, but it has led to numerous important discoveries in mathematics (related to more than one Fields medal), new ways to evaluate scattering amplitudes of relevance to the LHC, dual formulations of many field theories, phenomenological models of extra dimensions and cosmology, and recently improved understanding of complex systems in condensed matter physics also through dualities.