We spent Saturday undoing all the tree damage. I haven't cut the paint yet, but I did a test spot on the roof, and results are very promising indeed.
This morning. I reinstalled some hoses that had holes in them. I think I'll replace the main intake ducting hose with generic 70mm spiral hose, and delete the Venturi and cap off the vacuum amplifier.
I also started scrutinising the carburetor. The damper cap (black plastic bit indicated above) is broken inside, and doesn't seat very firmly, so I'll need to replace that. There was also no oil in it, so I added half a capful of 20W50 and now there is some resistance when trying to move the damper rod.
I adjusted the fast-idle stop screw as well. I am about to go back out and check if the mixture is set correctly.