Hi Andy,
No, I think the minimum level is designed into the part to keep the output stage transistors on while input has very small signal or no input signal at all (there is an additional current that is added to the detector summing node that lifts the output voltage to the minimum of 0.34 V; this is explained on the page 13 under the "RSSI Output Section" section). This comes into play while doing a pulse response measurement. Keeping the transistor on ensures that the pulse response has quick rise and fall times. If you really need a readjusted intercept that starts the output at zero, I would suggest a dual supply op-amp on the VLOG output like that shown in Figure 37.
There's no way to limit the limiter amp chain's bandwidth. That is set internally. The only thing you could do is put a low-pass filter on the input and/or slow down the output video bandwidth with a filter cap.
Hope this helps,
Joel