Update on the previous post:
Last night when the fire was pretty much dead, I did some more messin' with the oven door.
Opening the door a couple of inches made the exhaust, which was quite warm, cool down within a few minutes. If I shut the door again, it started to warm up again.
Of note is that I want to check the bypass to make sure it's shutting adequately; if it isn't then heat could leak out from under the cooktop into the exhaust. If I'd been on the ball when I was fixing the broken firebrick issue recently, I could've checked it then
As may be, having the oven door opened a bit caused the flue to stay cool so I left it like that, and before I went to bed I checked it again: the flue was quite cold and there seemed to be a slight cold airflow entering the oven and travelling across the bottom of the stove into the exhaust. Cold air doing that can't really have much effect on the heat output, I don't think, since the hot part of the stove is all above that level.
This morning when I went down and checked it, the cooktop was still a bit warm to the touch which I regard as a good sign. As to how much difference this makes overall, that would hard to test - but any obvious heat going out of the exhaust once the fire is out can't be helpful.