Deducing orbital degeneracy in geometries apart from octahedral or tetrahedral
The easiest way to do it is to look at what other people before you have done.

If you look at the $D_\mathrm{3h}$ character table, you see that $(x^2 - y^2, xy)$ transform together as $E'$.

I don't think there is a way of looking at diagrams of the orbitals and concluding that they are necessarily degenerate. As you said, there isn't "enough information to assume that the two parts add up to one".

It isn't really a limitation of crystal field theory, either. Crystal field theory isn't about looking at how much orbitals overlap with each other and saying "oh, I think those look about the same, they're probably degenerate". If that was the case then in an octahedral complex you would not be able to tell why $\mathrm{d}_{z^2}$ and $\mathrm{d}_{x^2-y^2}$ are degenerate, since the former only really overlaps with two ligands and the latter overlaps with four.

The degeneracy is predicted by symmetry, the application of which is integral to, and implicit in, crystal field theory. There is no CFT without symmetry considerations.