If I understand correctly, Toole finds that the indirect timbre should have less top-end energy than the direct, (conveniently) by a margin which corresponds with typical radiation pattern narrowing due to driver beaming. My own amateurish investigations have led me to a different conclusion: That the timbral discrepancy between the two should be minimal (even less discrepancy than Toole's findings indicate), and that BOTH should be gently downward-sloping. You are obviously vastly more experienced in real-world acoustics than I am, so I'd welcome your comments and corrections.
Nature usually has a rolling-off at high frequencies from a real source, because HF beams, of course, some things like strings don't actually have this characteristic, so there's always a question of "what's natural for the source". That's part of the issue.
Then the speaker, if you're used to an acoustic, you've learned to compensate for it, but for the boxes to have too much direct information with no indirect will suck you right "splat" into the loudspeakers.
May I ask you this: When you speak of comparing the direct vs indirect timbre, HOW exactly do you do so?
If you're listening, that's a natural part of learning to listen, between the hearing compression, precedence effect, auditory history, and the like. There are a lot of issues to consider.
If you mean analytically, you can measure the short-term spectrum of a room impulse response. It's more difficult to relate that to perception that one would like.
And, in fact, the diffuse vs. direct vs. "reverberant" is where a great deal of argument comes about, because the ear does not work like a meter, and there can be diffuse sounds that are not linearly independent as reverberant is supposed to be. (More on that in a discussion of analysis windows, etc.)
Could you go into some specifics about what intereferes with hearing "through" the listening room? THAT's the experience I'm aiming for, and any insights you can share would be greatly appreciated.
Biggest thing is to have the very first reflection from a room at least a few milliseconds later than the direct, and not even remotely specular. I've avoided that discussion because of the chaos upstream, but no, I am not a fan of specular reflections in a listening room, at all.
And I'm not a supporter of LEDE. That's both a question of physics and perception. That's also where an absolutist separation of "small" vs. "large" falls flat on its face.