Well, I'd say wet coal is better for dust control but that's about it. Moisture needs to be evaporated away, therefore robbing heat. While coal, being a solid rock, can burn wet, wetting it won't improve the fire/burn until that moisture is gone.
dampen it if necessary to lessen dust while pouring into the hopper, but it will probably dry out from the heat of the stove while in there. Wet coal is not recommended. my manual for the mag stoker has written at the bottom of every page 'do not burn wet coal' and i can attest that it will cause problems trying to get it to feed correctly.
heat distribution with a stove can be tough and is very much house layout dependent. There are a lot of threads on here discussing how people have overcome issues. I would suggest reading through some of those to see which is most similar to your situation and try a couple temporary things before cutting holes in floors and walls only to find out they don't work as well as hoped!!
...aside from heat energy required to convert moisture (water) to steam... steam takes up 1600 times the volume of water...which then needs to be evacuated with flue gases... ...more than likely though...damp coal will 'dry' before its actually burned... ...just my 2 cents
Is there any simplistic way to tie into the existing duct work--I've read a lot of guys doing it here- Maybe start a new thread--" using existing duct work" I'd bet you would get what you need as far as moving that heat
I tried to move the heat without any duct work and it futile. Grates,fans,open cellar doors you name it. Using insulated duct work up to a register did the trick. Also maybe the one reason why I bought the Super Mag it had a 100% blocking kit that stopped all air from blowing into the stove room and sent it up duct work. The side jacket's produce an airflow for the stove room but all the blower forced air get's upstairs. So my living areas upstairs stays perfect and the stove room is comfortable to work in. Blower doesn't work nearly as hard getting heat to upstairs.
I slightly dampen my coal in the bin with a garden hose and spray nozzle. As it is sucked down into the auger, it cut's down on the dust and seems to flow better through the auger and settle out in the hopper better.