When I reload onto hot coals with an active cat, do I still need to run in bypass mode for some period of time?
You do not need to run it in bypass if needle is well into active range. If needle is hovering on the lower edge of active, running it in bypass for 5 minutes while the wood catches on can still be a good idea, as that large charge of cold wood will likely bring cat temp below active. The needle won't show this, as it's too slow to catch transients much shorter than 5 - 10 minutes.
Bottom line, if you don't have a glowing cat within 5 minutes of closing the bypass damper on a fresh load of properly-seasoned wood, you probably closed it too early.
However, when I walked outside to check the chimney, there was thick white smoke belching out. Is it possible to overwhelm the cat with too much smoke volume?
Likely steam, not smoke. Oak at 20% MC still has 7 - 8 lb./ft3 of water in it. Assuming you fill a 3 cu.ft. firebox to 85% capacity, that's something like 19 lb. of water that has to come out thru your chimney.
However, yes it is possible to push so much smoke thru a cat that it can't process it all. No harm done, as long as it remains in active region.
When I am running low and slow to extend burn times, how low can I cut back the thermostat?
Until the cat stalls. I know it's not the answer you're requesting, but there's no one setting that's the same for all installations. Try running burns in consistent weather at progressively lower settings, until you find the setting that eventually stalls your cat out of the active zone. Know that this setting is dependent on draft, and therefore outside temperature. For a valid test, you must complete full burns without varying your setting mid-burn, as the cat temp (and stall point) varies through the burn. It will only take you a few days to find this setting, then mark it on your dial with tape or Sharpie.
When I did so, I could hear the knob click, and it looked like the fire was extinguished.
Perfectly normal, and not a problem. The firebox is producing wood gas, at this smoulder rate, and the cat chews the wood gas. A black firebox is not a sign of a problem, unless you shut it so far that the cat stalls. The click noise is the air inlet snapping shut. Your thermostat knob drives a spring which actuates the air inlet. In fact, you can find the knob setting at which you completely defeat the thermostat by turning down the thermostat until you hear a click on a cold stove. On a hot stove, this will happen at a higher thermostat setting, but that's okay.
