The "John D. Clark" in that story is the author of "Ignition!: An informal history of liquid rocket propellants", available from
https://archive.org/details/ignition_201612 and frequently posted on HN (see
https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... ).
That book describes a number of approaches with beryllium: https://archive.org/details/ignition_201612/page/n201/mode/2...
> Recently they have been experimenting with beryllium instead of aluminum. Combustion efficiency with these propellants, particularly the beryllium-based ones, is bound to be bad, since the chamber temperature is comparatively low. ... About all it proves is the willingness of rocket people to try anything, no matter how implausible, if they can con NASA or one of the services into paying for it. ...
> When the combustion difficulties are added to the toxicity of BeO and the price of beryllium, there isn’t really much point in continuing with it.
and with fluorine, in the liquid form: https://archive.org/details/ignition_201612/page/n39/mode/2u...
> The optimum oxidizer is liquid oxygen. (“Fluorine might be good, but its density is too low, and it’s a holy terror to handle.”)
and in an oxidizer that can decompose: https://archive.org/details/ignition_201612/page/n87/mode/2u...
> O2F2 [FOOF] had been reported but was unstable at room temperature ... [a list of other compounds, concluding] ... So ClF3 it had to be. ... It is also quite probably the most vigorous fluorinating agent in existence-much more vigorous than fluorine itself. Gaseous fluorine, of course, is much more dilute than the liquid ClF3, and liquid fluorine is so cold that its activity is very much reduced.
The next page (p74) describes an industrial accident with it, then its use in aerospace:
> The results were excellent, but the difficulties were infuriating. Ignition was beautiful —so smooth that it was like turning on a hose. Performance was high—very close to theoretical. And the reaction was so fast that you could burn it in a surprisingly small chamber. But. If your hardware was dirty, and there was a smear of oil or grease somewhere inside a feed line, said feed line would ignite and cleverly reduce itself to ashes. Gaskets and O-rings generally had to be of metal; no organic material could be restrained from ignition. Teflon would stand up under static conditions, but if the CTF flowed over it with any speed at all, it would erode away like so much sugar in hot water, even if it didn’t ignite. So joints had to be welded whenever possible, and the welds had to be good ...
and that's before getting to the "real difficulties."
Stross certainly read "Ignition!" before writing that short story - https://www.antipope.org/charlie/blog-static/2009/10/there_i... .