OK. It is good to obey the law where there are laws regulating what we do.For this specific post, I'm putting our views of what is and is not safe from a physics viewpoint aside, and looking strictly at what is law. Also, I'm not a lawyer and I'm not providing legal advice.
Within the United States, so far as I'm aware, there are no federal laws requiring ASME codes or standards be followed, they are completely voluntary . However, some states have enacted laws requiring ASME and other organizational codes and standards be adhered to, so builders should consult their state laws.
In Thailand, where I live, the governing standards body is TISI (Thai Industrial Standards Institute). I cannot find any standards regarding boilers or even "steam".
But I just follow the Laws of Physics first (So my efforts at making things do not break easily!) and then use anyone's standards and regulations where they have a strong Engineering background (better than my education and ability) as curiously, things like ASME regulations have a lot of simplified Engineering in them. (e.g. it is very difficult to work out appropriate stress concentration factors, so ASME just use "3.3" for simple SCF applied to material stresses of Steam boilers with penetrations). However, I will deviate in special cases where the "global" assumptions are not very appropriate.
There are loads of technical papers - by some very clever and able people - that explain lots of equations to be used in special cases, so I use those as well, if I find something suitable. e.g. I recently found a method of determining the stress in a rectangular tube subjected to internal pressure. This suited a model I was given that used extruded rectangular brass as a boiler tube.... so I did the calculations and they were a better result than my previous "estimations" - but confirmed rather than changed my NWP of that boiler.
I thought your fabricated spiral radiation plate was ingenious, but just needed thick copper sides to withstand your proposed system pressure... Assembly is difficult, as you explain, but that is something within your workshop and skill capabilities - or not - as suits. I would have considered using a paste flux and brazing filler material. Oven Brazing is a process I have worked with in industry - assemblies of steel pipes were made on jigs with Brazing paste, then passed through a long oven by conveyor to heat and cool in a controlled cycle and all the finished parts were pressure tested. Statistically, they had less than 20 pieces per million failed. A very controllable process, not requiring a high skill level.
Enjoy the "hobby", and keep on with your very ambitious designs. I enjoy the discussions and learn a lot from you.
K2