Haining certainly shows a ring of rivits top and bottom which really only need be pushed into the hole and the protruding inner end bent so it does not fall out. This does not close up the layers of copper so provided they have been fluxed before inserting the rivits the solder will flow into the joints as well as soldering the rivits into place.

An alternative is to use a higher melting point solder to solder the rivits into the barrel ONLY. You can then flush them off on the inside and then treat it as just a plain tube into which the flanged top plate and foundation ring etc can be soldered.

If you want to go the whole hog and add vertical and horizontal rivited joints I would be tempted to make them up by soldering rivits into a strip of copper for the vertical and a ring for the horizontal. Again flush then off on the inside and place the strip and ring around the boiler and solder to the barrel when you do the other joints.

If the boiler is already made then it will be difficult as even dunny strips and rings will need fixing with something to resist the heat. Might have to think about completely cladding the boiler in two half round sections each of which could have dummy rivits soldered in and just find a way to retain the two halves. I have seen this method used on portable engines.

Stick dummy heads on with jb weld?

According to https://en.m.wikipedia.org/wiki/J-B_Weld it’s good for 260C which is a lot hotter than the steam we’re likely to use. Never used it myself.