Well, I think we tried everything remotely. Next thing would be to have someone look at your boiler.
I have the same NCB 250 coal, with the difference of stainless steal shaker grates I guess.
Mine works awesome as long as I use good coal; Blackshack anthrocite. (when I was using crappy bit. coal, I was ready to return the boiler. It was awful. Fire dies out in 8-10 hrs, lot of nasty smoke, lot of ash, etc.)
There is like no smoke at all with the anthrocite. No ash either. Just a very fine powered.
I much much much prefer burning anthracite over wood.
As soon as I switched to this Blackshack anthrocite coal, and I changed my settings all my problems went away ;
new settings 10/2013 to resolve the issues;
172/5/100-80% draft open/
house at 72F,
and I load the coal in the middle,
shake it once a day gently,
load at 9pm 6 shovels +1-2 logs at most,
top off with 4 shovels of coal at 7am, all is good. I can go 20-28 hrs with coal.
I had all the same issues as you, before this. I have not touched any of the setting for 2+ months, because all is good now.
There has to be something with the boiler.
All it needs is fuel, and air for the coal to burn.
I wonder if your draft opening keeps getting clogged since it was clogged before.
Don't load the coal or wood all the way in the back.
Have you taken the blower off since last time you de-clogged it? It would be interesting to see if it is clogged again.
I would open the draft all the way. The only reason a coal fire would go out, if;
#1 out of air,
#2 out of fuel/coal
It almost seems to me that it is out of air, that's why it goes out so quickly.
With your settings at 175/3 that blower is coming on pretty ofter even when it's warm outside.
Mine is at 172/5 and it never goes out. I have heat and water hooked up at the house.
When I had my differential higher 180/12 my fire did go out. It was because, coal over shoots the high temp.
So it would start at 168F, get a very hot fire, shot off at 180, but the hot coal would heat the water to 188-190+, than it would idle till water drops to 168F, which is 20F difference, that could take a long time to drop to.
I have a termometer set up that is 0.5F accurate, and now with 172/5 setting; I get 170-165, sometimes if I open the load door 161F.
My house is at 72-74, and all the hot water.
So, I think your settings are good.
I'd look at the draft again, open it more, and check if it is clogged (take blower off, and stick the broom stick in to see like last time). May be shop vacuum it out from both side, ash pan, and blower unmounted.
After that, new boiler…