Well, with a tall chimney you should have good draft, with the barometric damper, it should be good and consistant draft. With these, you should be able to close down the air to the coal quite a bit and get it to just idle along.
Most of the guys who use a firebox reducer have a huge firebox, like Cap, who has a Harman SF250, which holds about 120# of coal!!.. His firebox is roughly [I'm not sure about these diementions] 15" wide, 26" deep [front to back], and can be filled about 10" deep. A LOT of coal. He builds a false back wall at about the halfway point, making it about 15" front to back.
Not all fireboxes lend themselves to this process. Take a look in your firebox, move the grate shaking handle, is there a ledge on the sides of the firebox between the grates and the firebrick that you could rest a flat steel plate, covering the grate from side to side but NOT restricting the shaking action of the grates?? Cap's harman has a raised steel ledge that works perfect, he cut a piece of 1/2" steel to go from firebrick to firebrick, resting on the steel ledge, the grates can move below the plate unhindered. He then stacks new firebrick on the front of the steel plate, makeing a new rear wall to contain the coal. I think he backsup the firebrick with more bricks back to the original back wall. Firebrick are cheap, about $1.50 each. Last forever as long as you don't drop them!
A smallish fire for the cool autumn nights is a good idea, You may do fine without a firebox reducer, or may decide your want one.
I hope my text description makes sense, The bottom line is you have to block off all air coming up through the grates except for under the burning coal. a coal fire will go out without air being drawn through from underneath. so as long as you can block off the rear portion of the grates and make some sort of firebrick false wall, then you should be OK
Take care, Greg L