The part I didn’t understand turned out to be the bandwidth of the final output stage = “video bandwidth”, which defaults to 25 MHz. After fixing the input circuitry, a 25 MHz VBW let the output track a 60 kHz input signal just fine:
Adding a 56 nF cap across the C6 terminals (just above the AD8310) lowered the VBW to about 1 kHz:
Which flattened that sucker right out:
The ripple for an absurdly high amplitude 32 kHz signal amounts to 36 mV:
Firing the tracking generator into the input with a frequency sweep from 100 kHz to 250 MHz shows the low end looks much better:
There’s a slight droop across the sweep that might amount to 50 mV = 2 dB, which I’m inclined to not worry about in this context.
Applying the attenuators once again produces a scale factor of 23.5 mV/dB across 30 dB of RF, but this time the 60 kHz output makes sense, too.
Using the typical output curve from AN-691, that 2.0 V output corresponds to -13 dBm, which sounds about right for the tracking generator (which might really be -10 dBm).
I must calibrate the log amp output to find the actual intercept point (nominally -95 dBm, but could range from -86 to -102) at 60 kHz. The intercept is the extrapolated RF input producing 0 V out, which then acts as an offset for the voltage-to-dBm calculation; you start by finding the slope of the voltage vs. dBm line at some convenient power levels, then solve for dBm with V=0.
So a cheap AD8310 Log Amp module from eBay can work in the LF band, after you rearrange the input circuitry and tweak the chip’s filters. At least now I have a better understanding of what’s going on …
The Smell of Molten Projects in the Morning 
Nice looking results, Ed.
I found a possible clue to why the original input topology was used — there is a somewhat similar part from AD, the AD8313 demodulating log amp, that recommends putting the termination resistor across the device input pins. Quoting from the “Input Coupling” section of the datasheet (page 16), “It is preferable to place the termination resistor directly across the input pins, INHI to INLO, where it lowers the possible deleterious effects of dc offset voltages on the low end of the dynamic range. At low frequencies, this may not be quite as beneficial, since it requires larger coupling capacitors.”
So maybe the layout person picked up the wrong data sheet and that is where the mistake crept in. Who knows.
Makes sense to me. The coupling caps in the AD8313 datasheet look like a few mΩ at 100 MHz (the low end of its range), not the tens-to-hundreds of Ω for the ones on the AD8310 board (at the frequencies I need), so they fade away against the terminator.
I suppose I’m just using the AD8310 circuit outside its “design range”, although obviously you can’t figure the range from the sticker atop the can.