Somebody should have thought of this, and it turns out that somebody did.
A couple of years ago, I wrote about setting up a network boot server on my home LAN. I said this meant "taking the job of doing DHCP away from the router and doing it myself on a Linux box".
Reader, I was wrong.
Setting up my new connection from BT today, I really didn't want to keep running DHCP separately on a Raspberry Pi. What I wanted was for the Pi to just talk to clients which wanted to do network boot, and leave the BT router to do DHCP for ordinary devices.
This exists, and it's called proxy DHCP. dnsmasq on the Pi can handle it; this tutorial is the one I got working. Sadly proxy DHCP doesn't seem to honour options, so I had to take the path prefix (option 210) and manually prepend it to all the paths in my boot config.
This is all back up and working now, and hopefully should prove useful and less disruptive for a few years yet to come.
Now that i have native IPv6 and DHCP is back on the router, the Pi ceases to be a single point of failure, though it's been rock solid for nearly three years now.