I deleted your edit in which you added extra information about your speculation about the parts used. Before moving on to technical details, I want to comment on your behavior in case you do not realize how poorly it is coming across to us.
You are a guest on this forum. We made it clear we do not want to give out the details of the parts involved, and you proceeded to post them (or something close to that) here. I really do not understand what you thought you were going to achieve by doing that. If I went to your house and you asked me not to do something there, I would not do it or I would leave, independent of my assessment of how reasonable your request was.
Regarding your broader response, we have no problem with criticism and your expressing your perspective even if it’s negative or disappointed or whatever. Obviously, we are aware that people prefer us disclosing all kinds of things. Likewise, you must be aware of at least some reasons to keep some information private and that there might be additional reasons you are not aware of. If there were some obvious right answer for how to weigh various pros and cons, everyone would probably be doing the same thing. It’s helpful for you to add weight to a pro or con (even if it’s as basic as saying, hey, I would really appreciate it if you guys shared more details); focusing on just one side as if it’s the only factor is not very useful.
On to the more technical aspects of your posts: Nathan had a much longer initial response with all kinds of details, and I reminded him that he is not supposed to be putting a lot of effort into a particular assumption without getting some basic information. “The MOSFET does get hot very fast” does not give us much to work with, especially for an item that is expected to get hot. How hot? How fast? And the thing is, we’re not necessarily asking for that (though it could be helpful). But “the MOSFET went up in flames”, or even the less dramatic, “the MOSFET broke”, at least identifies a problem.
I appreciate that you included the specificity of the 100J, which might be a clue that that is just too much for this product (for instance, if that 100J has to get dumped over 5 seconds, that would be 20W, which is beyond the limit of this regulator). Your guess about the component involved (which I deleted) should give you a hint that the regulator probably does not work exactly as you initially assumed (the MOSFET is intentionally getting used in linear mode), so if there is a problem with the design, it’s not exactly what you suggested in your posts.
So, it’s possible these regulators just will not have the power capacity your application needs, in which case there is not that much we can do. It’s possible the external resistor version could work. If you want to troubleshoot this more, please confirm that the MOSFETs indeed went up in smoke and provide some information about your system.