While I was looking at this on the board this weekend, I noticed that C diminished and Gb diminished are the same chord.
So in terms of what the official related diminished chord is for Ab is concerned, I don't think it matters because you'll end
up with the same triads no matter which note you use, namely ... C,Eb,Gb,A.
And in addition, I also noticed this... if the dominant of the chord that you are voicing is major in the key that you are
playing in, then you can use a major third to find the diminished family... and likewise, if the dominant of the chord is
minor in the base key, than you can use a minor third to find the diminished family:
I'll stay with the key of C#, like the rest of the thread... if we are voicing Ab, we take the dominant which is Eb... now,
Eb is minor in the original key of C#, so we take a minor third, which is Gb... and this gives us the related diminished family...
now, if we wanted to voice C#, we take the dominant, which is Ab... and since Ab is major in the key of C#, we then take
a major third, which gives us the diminished family of C.
Diverse, I noticed in this thread, that you seemed unsure of when to lower notes on the third of the dominant when
finding the related diminished family... well using the method I mentioned, I find that I don't need to lower any notes at all...
the major or minor third rule gives you the diminished family of roots on which you build your right hand triads without lowering
any notes... try it.

And then, there's one more thing that I noticed... if the dominant of the chord that you are voicing is minor is the base
key, then you can use the major third of the root of the chord you are voicing to find the diminished notes... so look at
Ab in the key of C# again... the dominant of Ab is Eb, and since Eb is minor in the key of C#, we can use the major third
of Ab to find the diminished notes... the major third of Ab is C... and even though we can say that the relative diminished
family of Ab is Gb by the dominant method above, C diminished is still in that family, as I stated in the beginning of the post...
and therefore we end up with the same family of notes to build the triads on... now look at C#, the tonic... we've already
determined earlier that the related diminished of C# is C using the dominant method, with Ab being the dominant of C#...
now, since Ab is major in the key of C#, we cannot use the major third of C# to find the diminished family... let's try it...
the major third of C# is F, and F is not in the C diminished family... so the shortcut appears to work only when the dominant
of the chord being voiced is minor is the base key that you're playing in...

So there you have it... and I'm no expert... in fact, I'm a beginner in theory... studying to show myself approved unto God...
So Diverse, and all ya'll... am I way off track, or is this making sense to somebody?

God bless,
Eggs