I've done several experiments looking at the forces the vibrating string produces at the saddle top, and how changing the string height off the top alters the sound produced. As always, it takes a fair amount of effort to figure this stuff out, but not much time to describe the results.
The largest 'signal' that the string produces at the saddle top is a 'transverse' force: across the length of the string. Basically, if the string is moving 'up and down' relative to the plane of the top, it pulls the top 'up and down'. The string can move 'across', parallel to the plane of the top, as well, of course, but it's hard to move the top that way, and it doesn't produce much sound. The 'vertical' string motion makes the lower bout of the top move like a loudspeaker, which is very effective at making sound. This is why you try to push the string straight down in a 'rest' stroke; so that it will end up moving 'vertically' as far as possible. The actual force the string puts on the bridge to pull it up and down depends on the amplitude and where you plucked it: at most it would be something like 10% of the tension of the string 'up' or 'down' initially.
The string tension also changes as it vibrates; it's higher when the string is either 'up' or 'down' (or 'left' or 'right' if it's moving horizontally). Thus the tension change is a double the frequency of the transverse vibration; an octave higher. The relative amplitude of the two signals varies for different strings, but it averages something like 1/7 of the force of the 'transverse' signal. This twice-per-cycle tug on the top of the bridge rocks it forward, toward the nut, and causes the top to belly up behind the bridge and dip downward a little in front when the string is displaced. This is a less efficient way of making sound than the 'transverse' force for several reasons. One is that half the soundboard is moving 'up' while the other half moves 'down': some of the sound is cancelled out. Its also much harder to tip the bridge like that than it is to push it inward: luthiers build tops to resist that tipping motion because that's what breaks tops. This, along with the smaller force, means that this 'tension' signal doesn't produce much power compared with the 'transverse' force signal.
There is also a longitudinal compression wave in the string, which is produced whenever you pluck it anyplace but in the exact center of it's length (in other words, it's usually there). You can think of it as sort of like a pressure wave in a long, thin pipe. The pitch of this depends on the material and construction of the string; the tuning of the string hardly effects it at all. Normally, with nylon guitar strings, it's up around the 7th or 8th partial, but, obviously, it can vary. Because of the peculiar way it's generated the power of it depends in part on how it relates to the tuning of the string. It can 'come and go' if it's not lined up in pitch exactly with a string partial, and it matters whether it's closer to an odd or an even one. This string signal works on the bridge top like the 'tension' signal.
The higher the strings are off the top, the more leverage there is for the 'tension' and 'longitudinal' signals to drive the top, so raising the saddle puts more of those frequencies into the sound. In particular, you get more of the second and (sometimes) the fourth partial, and also more of the high pitched 'longitudinal' wave frequency. The second and fourth partials would probably add some 'fullness' but the longitudinal wave is often dissonant. It's also in a high frequency range where your hearing tends to be acute, so you pick it up. When it's very close in pitch to an odd numbered partial (often the seventh) it can 'couple' in strange ways with the other string vibrations, and cause things like buzzing on every note. And, of course, the seventh partial is dissonant anyway. I suspect that's the source of Romanillos' 'banjo-like' timbre.
In my tests, people listening to recordings of well-controlled mechanical plucks were unable to hear changes in break angle, but picked out changes in string height off the top virtually every time. I didn't ask them to describe the sounds; just to say whether they were 'the same' or 'different'.
Measurements of those plucks showed that there was not any more power in the sound with the tall saddle, nor did changing the break angle alter that. What changed with changes in string height off the top was the mix of frequencies in the signal, with, as I say, more of the second and (maybe) fourth partials, and the high-pitched 'longitudinal' wave, when the strings were higher off the top. The power in the string, and the mix of partials, is set by how and where it's plucked, and the amplitude, and the efficiency/effectiveness of the guitar in turning those string signals into sound seems to be pretty much fixed for a particular instrument as well. If there's more sound at one frequency there seems to be less at others, all else equal, so the power stays the same while the timbre changes with string height.
Of course, this is a pretty condensed account, but it hits the main points. As with any experimental finding, it's provisional: if somebody does a better experiment and finds something different we'll have learned something. At the moment, though, that's my story and I'm sticking with it.