Generally people tend to burn the wood fire too long, before throwing the coal on. It's a coal stove, not a wood stove. Light the wood kindling using paper or cardboard under it, KEEP THE ASH DOOR OPEN, when it gets going good and roaring, throw a good deal of coal right on it. You don't need "red hot coals" that take 2 hours to get, from burning 20 large logs, before throwing coal on- that's not necessary. I start my stove every year, with a small pile of kindling, that would barely fill a 5 gallon pail, picked from my back yard - and never use any logs. Keep the ash door open, keep it ROARING, and throw some coal on. Keep the door open, the coal starts crackling and will ignite in about 5-10 minutes. Throw more coal on, keep the door open. In 20 minutes you'll have a coal fire. At that point you can close the ash door and set the draft at 3/4 turn open if it's a rotary draft control.
Provided, I have a good modern stove, and modern double wall stainless chimney. Like the old saying goes, you can't make chicken salad out of chicken crap. To get a coal fire going quickly in 20 minutes, requires a good stove and chimney in the first place, that's the premise.