I finally bit the bullet and did a factory reset at the end of last week. I chose to let my apps be restored afterwards. It took a long time to reboot after the purge, which worried me, but finally the coloured balls stopped spinning, the Android logo appeared, and all was well. There were a few things that I had to restore manually (Google ID, some IDs and passwords for online services like banking, Twitter, Dropbox, and my main WiFi settings) but it wasn't as bad as I'd feared.
Overall, I think it helped, especially with battery life. There's still some lagging, especially when apps start up for the first time after the device is switched on, but once apps are running the device is quite responsive. It's probably as good as it gets, given the ageing hardware and only 1GB RAM.
I do switch my N7 off quite regularly, so my experience might be different from that of people who leave theirs switched on all the time. I do sometimes delete some of the entries in the 'Recent' screen in case they're taking up too much memory (I don't know if they really do).