Here's the science bit. I drew this after I connected all the above in every possible combination until it worked. I don't really know how it works, or why it works, but who am I to question it? Nothing has gone on fire yet, and it does exactly what I want.
I think it's likely that it works because of the bi-directional nature of the HDMI switches. After all, it's printed on the top, isn't it! So one of the switches is converting one input into two outputs, and the second switch is converting two outputs into one input. I think.
Anyway, the point is that I have split the HDMI at the RGBtoHDMI point to go to the joiner cable which then goes to the second switch and to the PC capture stick, whilst at the second switch the output goes to the monitor.
By choosing between the two selections on each switch, I can direct the Beeb's RGB output either to the monitor only, which is what I need when the PC isn't doing capture, OR to both monitor and PC capture.