I'm not sure if I understand exactly what you are asking, but it seems like you want to learn how to recognize the chord degrees within a key, am I right?
I can just about vaguely hear two tones at the same time
Imho, it's more important to identify harmony by their respective characteristics, rather than their individual notes, because it's easier to identify a chord degree by its distinctive sound rather than hearing every single note and then figure out what chord that really is, just like it's easier to identify intervals by their sound, rather than figuring out which exact two notes are played and then measure their distance.
What other methods would be more efficient
There are plenty of programs that can help you recognizing chord degrees within a specific key. EarMaster, for example, has a chord progression training, and with smartphones nowadays, there are plenty of apps that can train you in recognizing chord progressions and thus learn to recognize the characteristics of certain chord degrees.
If you'd follow the order of EarMaster, it's best to start with chord identification - identifying whether you hear a minor/major/augmented/diminished/seventh/etc. chord - followed by learning to recognize these chords in their different inversions and eventually learning to recognize chord progressions.
is it even possible to cultivate it to excellence beyond childhood?
Ear training is something (nearly) everyone can learn, and obviously as we grow older it becomes harder, but almost everyone has the ability to develop a sense of it. The best way to do this is by practicing every day for a few minutes. Whether it's possible to become entirely proficient in ear training is probably something that differs from person to person, but I guess that if there's a will, there's a way?
A few tips that can help you practice:
- Learn to recognize the scale functions. So let's say you listen to a tonal melody and you pause it at some point, try to figure out by ear which tone of the scale that last tone was by singing the descending scale to the root, starting from that tone and counting the amount of tones sung.
- For recognizing inversions: try to sing the chord you're hearing or playing in an ascending arpeggio from the bass note. Try to find out the interval between the first and second note, and then from the second to the third note (and third to fourth in case of four notes, etc.). Using your theoretical knowledge, you can figure out what inversion it is, and practicing this a lot will make you more familiar with the sound until you can actually hear the inversions.
I hope this more or less answers your question, or at least pull you one step further through your journey!