We feel your pain, Alan.
It sounds like you have a pretty good understanding of things, but feels to me like maybe you're trying a little to hard? I don't know whether this will help, but you said any and all advice, so here goes.
First: stop messing about with the nut. If set too low, it really only affects the open string and first few frets; if too high, it will increase your action overall, but not by that much. So just set it high enough to get the plink as you describe, and leave it alone until you get the rest of this sorted out.
Next: don't worry about the string gauges. As long as you can get adequate relief in the neck (and .016 measured as you describe should be fine), then you have enough string tension. From what you say, it sounds like with the lighter strings, you can get this relief and still have at least a tiny bit of tension on both truss rods. As long as that's true, then you don't need heavier strings.
I'll qualify that slightly... heavier strings will generally be under more tension, and therefore won't move through as much of an arc when plucked, and so they might buzz less if you're right on the edge. However, the difference in going 40-100 to 45-105 should be small enough that you could raise the bridge slightly to compensate, and not feel like the action was excessive.
So I would suggest sticking with the strings you like, as long as you can still get enough relief in the neck.
The one thing that sounds funny to me is when you say action was approximately .060 on the E string at the 24th fret, and .090 at the 24th fret on the G string.
How did you measure this? I think the usual convention is to measure action as distance from string to fret, at the 24th, without the capo at first fret (i.e. just measure the open string, while in usual playing position).
Your numbers seem ridiculously low to me, especially for someone with a moderately aggressive touch. Joey's classic post on the subject suggests 1/8 on the G side, 3/16 on the E. If my math is right, that would be 0.125 on the G, and 0.1875 on the E. This is twice as high as you're describing - though reversed from thin to fat!
I can personally go a little lower than that, and in fact after recently raising my bridge because I started digging in a little more, I'm still under 3/16 on the fat side (a B, in my case), and the G side is right at 1/8. Granted, I'm fretless and it's a little different, but 1/8 G and 3/16 E is not exactly what most people would call high, let alone unplayable. It's a good starting point.
Again, maybe you measured with the capo still on, which would be different, or maybe we just have a typo here. Can you confirm?
Perhaps the best advice I can offer is to forget about the holy grail of super-low action. What you want is an instrument set up in such a way that you can have a good time playing it. I just got over this syndrome myself recently... kept trying to get the neck straighter and bridge lower, and I could do that as long as I played with a very light touch and lots of volume. But I wanted a wider range of expression, and more deliberate plucking, and then I would get this very subtle but highly annoying buzz. So I raised the bridge a 1/2 turn or bit more and eased in about 1/8 turn on the truss rods, and as long as the action police don't come over to measure things, I'm happy.
Sorry for going on. To summarize, it sounds like you have a fairly good setting for the nut, relief of .016 as you measured it sounds great, you should stick with the strings you like. I suggest you leave these things alone for a bit, just to reduce the number of variables.
The only thing that seems odd to me here is your action measurement, though maybe you measured differently than I do. I suggest you try the 1/8 G and 3/16 E, measured with the string open and in playing position, and tell us how that goes.
I know I'd rather have the action a little high and be able to play cleanly, as opposed to getting nothing but buzz. It might be better to start that way, get settled in, and then start slowly working your way down again.
Good luck.
-Bob
(PS: I have no clue what happened when you switched between strings, that sounds really strange.)
