It is quite amusing watch you two fight about liking or hating tubes. Why does anyone HAS TO like / dislike tubes? There are many ways to skin a cat (wrote he while the cat is sleeping on his feet...), neither of which has to be considerably the better one. both have pros and cons. As far as I see it, Tim just states the fact that it is not necessary to use a tube for the application and he personally would not do it, I guess mainly because of his experience designing circuits with semiconductors which alows him to design a suitable circuit without any problem.
But: If we are looking for a simple, cheap'ish, beginner proof method to build a high'ish voltage PSU my best guess would be that this will be used for tube experiments. So there should be tubes available for the person interested in this project which is the reason I PERSONALLY would choose tubes for the pass element, as they are relatively easy to get, potentially even in the future thanks to audiophoolery (and yes, i for myself like tube amps, so don't you dare to take offense from that!) and quite easy to handle compared to most modern FETs and IGBTs which are often only designed for switching purpose with no SOA for linear applications which would make them pretty hard to substitute for a beginner not knowing how to judge if THAT particular FET in his hands is suitable or not. For the U/I regulation circuit I would, whatsoever, choose semiconductors. That should not be too hard to do with jellybean parts.
I would also make restrictions to the voltage range. Why the hell would you need 0-350V? I would much prefer something like 100-600V for tube experiments. Could simplify the circuit a bit. Right now a very crude, old regulator based on EF80 and EL34 which i build years ago is sitting on my bench, that one outputs around 150 to 450V. I found myself more often limited by the 450V than the 150. The region between 60 (standard for most dual voltage lab power supplys) and 150V is not that commonly needed, at least for the projects I work on.