Have any "toy models" of detecting string theory in other universes been identified? Someone could publish a paper tomorrow saying, "This choice of Calabi-Yau manifold recovers the physics of the observed universe, and implies this feasible way to detect how the universe's string-theoretic nature differs from vanilla GR+QFT". The first part is unlikely to happen soon, if only because there are so many choices of Calabi-Yau space to consider, some of which have already been shown to predict a different universe. But this question focuses on the second part. Are there any known examples, however alien the results may be compared with what we see, that meet the following criterion?

If that choice were correct in some universe, that universe would look like GR (or a suitable alternative classical theory of gravity) plus QFT (with a suitable particle zoo, parameters etc. that would be that universe's "standard model") in appropriate low-energy limits, but string-theoretic corrections would be observable under suitable conditions?

In particular, I'm hoping for an example where the specific beyond-ST limits have been computed, and we can imagine physicists in that universe discovering those first and then realizing how to observationally merit ST with that choice of a CY manifold.
Effectively, this question inverts a common way of thinking about experimental probes of ST. Instead of searching the landscape for something that looks like us, we choose a starting point, imagine being in that universe, then wonder whether, should local physicists correctly guess the chosen starting point, they could feasibly test it. I don't know much about the classification of CY manifolds, but I imagine some "simple" ones make for easier calculations, albeit not necessarily ones that make string-theoretic corrections to the low-energy limit easier to access. I'm hoping at least one researcher has tried this, with the motive of illustrating that string theory could be easily tested in some part of the landscape, even if our own Universe doesn't make it easy.
 A: The choice of some CY manifold does not uniquely determine the parameters of the 4d effective theory after compactification. This is because given some CY manifold there are plenty of possibilities to choose the flux parameters (in type IIB string theory $F_3$ and $H_3$, in F-theory $G_4$) in order to fix the moduli. Typically, in research papers you choose some rather simple CY manifold in order to make further computations as explicit as possible. In this way, you can do a proof of principle (e.g. showing that you can in principle implement the Higgs mechanism etc.). However, it is very hard to find a solution for the flux numbers such that you discover our whole universe, see e.g.
https://arxiv.org/abs/hep-th/0602072
Nevertheless, one can make connections to the real world. For instance, in the large volume scenario (a mechanism to obtain string vacua at rather large CY volume) there is a light axion which will contribute to the effective number of relativistic species $N_{\text{eff}}$, whose value in the standard model is $N_{\text{eff}}=3.04$. The light axion increases this value and easily results in a contradiction to cosmological measurements. This example may give you an idea that generic features of some corners of the string landscape can easily contradict real world. In this case one needs to look at other corners.
In the context of the swampland programme one aims at delineating the string landscape from the so-called swampland. The latter contains all 4d effective field theories which do not admit a reasonable UV-completion. As a result of this swampland programme there is evidence that string theory may forbid sufficiently large tensor-to-scalar rations during cosmological inflations (such as $r>0.1$).
To sum up, I think the best way to test string theory is by finding a no-go theorem prohibiting some feature of our universe. If this feature is found in real world then the no-go theorem is falsified. If it is sufficiently generic, it may even falsify string theory.
