Oh I dunno, I think Vermiculite fill would be a good idea, as you'll get notice when your steel liner eventually disintegrates and the Vermiculite blocks the remainder of the liner. Really, the last thing you want is a hole in the liner with no fill as that could cause you lots of trouble down the line.
If it was mine, I'd get up on the scaffolding, stuff a liner down it and backfill with vermiculite, install the burner, stick a pot on it and flaunch it and light it up, making sure it's fired correctly with well seasoned wood.
I wouldn't use kiln dried because of the environmental issue, and also because a lot of kiln dried timber comes from Russia. So not are you negating any carbon offset with the forced drying, but you're also adding 1600km+ and a trip in a container ship to the pollution. Luckily I own several small Birch, Beech and Hazel coppice, so it's easy for me to say that.
<cough> Even though I have a lousy splitting technique, I still manage OK. </cough>
So really, you'd do well to get Lars Myttings book, reading it and following the firing instructions and try to source a quality supply of local coppiced hardwood. Initially you may have to buy kiln dried to start burning now, but if you've got the space dry it yourself for next year. It takes a bit of effort, but if you care about carbon offsetting, it's the only way to do it. Even so, it won't ever be carbon neutral, as you've still got to transport it from somewhere, unless you plant way more than you consume.
If you have a steel flue liner, stay clear of kiln dried Oak and Sweet Chestnut, as they become highly acidic after being kiln dried and are best air dried.
I wouldn't put it off any longer and just get on with it. The leaks will hopefully be fixed when the pointing is done in the spring. What you need now is lots of heat to start drying it all out or it will just get worse and you'll end up rotting some timber somewhere if you leave it.
You'll need to fire a lot when you have a leaky stack though.