This is a great site for sharing info, I don't have a coal stove and never had one.
But I want to share a experiance I had about 15 years ago that may help you more evenly heat your house using your coal stoves.
Years ago I built a c shaped manifiold out of 1" black Iron pipe and installed it in my fireplace in place of the grate that you would normally build a fire in.
I connected the manifold to my heating zone of my boiler with another circulator.
I had a switch that I would switch on when I was going to build a fire in the fire place and that would turn on the circulator.
So the fire in the fireplace would heat the water and that would be circulated around the baseboard thru-out the house.
It turned out that I didn't need much fire in the fireplace to keep the whole house comfortable.
As a matter of fact I found my self opening windows alot.
If you installed a DHW coil in your coal stove but instead of making DHW , hook up a circulator and connect it to your baseboard you will be doing the same thing I did.
As long as you have a coal fire burning you must leave the circulator running.
You will probly need a battery back up on that circulator incase you loose power and your coal stove keeps burning
so you don't start making steam.
If you have a stoker I think it will shut down by itself but I don't know if it shut down fast enough.
This is something that you will have to work out.
but I think it would help you spread out the heat more evenly.
I noticed you can get differant size DHW coils, I would get the biggest one available for this job.
Hope this help ya!