> are all the different kinds based on converting the AC amplitude to some sort of DC and then using that as a control voltage?
Most of them.
> Are there any designs that just process the AC as is to accomplish limiting?
In the LA-2, audio AC drives a lamp which shines on a photo-sensitive resistor, which reduces gain. No DC voltage is derived. BUT: the lamp goes bright on both sides of the AC wave, so this is "rectification". And the photo-resistor is slow to turn on, much slower to turn off, so this is time-constant. It is not done electrically (and is practically un-adjustable), but it works the same as a rectifier and time-constant network.
> It seems like you could make a device with theoretically no attack or release times, just a threshold and compression ratio, but I really have no idea.
That is clipping. Play your 10 Watt amplifier at the 1,000 watt level. The peaks will be flattened. This is what you would get with zero attack and zero release: gross distortion. We can do that a whole lot cheaper than a proper AGC system.
A slight variation is a hyper-fast attack and long release. Now the initial rise-time of the first loud note is "clipped": it rises to the threshold and then flat-tops. But after that (until the release restores gain) the waves are perfect, just smaller than they came in. That's probably the most transparent way to limit peaks, if you are not trying to raise average level. But these kids today want their records LOUD, so they use a short release so the note-decay is brought up, and a non-zero attack so the initial transient clips and sounds louder. Most "musical" settings are between these two extremes. There are also "odd" settings like a very long attack and instant release, rarely useful for special effect.
To get back to the question: we want an "average" of many cycles, not an instantaneous clipping. There may be many other ways to do this, but in analog electronics the simplest is to capture the peaks (peak detector), bring both + and - peaks to the same polarity, and integrate (average) them with an R-C network. We want asymmetrical integration so we use a small series resistor and a large shunt resistor to give a quick attack and slow release. We also want no effect on soft sounds, so we add an offset voltage somewhere and only reduce gain when the integrated voltage is above the offset.
> "automatic gain control" using diodes (but also going back to using a DC control voltage).
That's one of the several ways to do it. The dynamic (small-signal) resistance of a diode is related to how much current flows in it. If the signal current varied the resistance, it would cause distortion. Indeed a common clipper uses diodes. But for smooth AGC, we flow a large DC current and a small audio current in the diode. If the steady DC current is much-much larger than the audio current, distortion is very small. To reduce gain, we flow an even larger DC current, the diode dynamic resistance goes lower, and the audio signal comes out smaller. For this to work you need significant gain somewhere to generate/control the large DC control current from the integrated audio current.
