ETA: Installed a new version of Stuffit on the G3, had another go at unpacking the .sitx.hqx, and got an Error #17540 (format error). Some very brief and tired Googling suggests that this is Stuffitese for "SNAFU". I tried running the BootX app (which seemed to have been unpacked despite the error) but that gave an error of type -39 (eofErr), so obviously didn't unpack properly.
I mean, look, be honest here, am I just being dim?
I have already set a possible Plan B (the "acquire more tractable hardware" plan) in motion, but I am going to be mightily pissed off if it turns out that the G3 is more stubborn than I am. Or cleverer.