Just installed Linux Mint 19 and now using it to post this. It worked straight out of the box and it's sprightly compared with what I remember of the previous.
I suspect the gradually-slowing-down came as a result of incremental updates and version upgrades over successive months, as the OS gradually came to need more system resources. It's standard behaviour with Windows, but I noticed it with full fat Ubuntu too. Didn't happen with Lubuntu - instead an update completely broke it.
I'd forgotten about PuppyLinux. I've used it in the past to revive old PCs so it's good to see the community is still developing it following Barry Kauler's retirement. The interface always looked a bit, erm, quirky but, boy, was it a fast OS.
Anyway, looks like I'll have a year or two more of use out of this netbook.