Well this kinda blows...
Currently, with all appropriate drivers installed, this 1440p monitor is working like a magnified 1080p monitor with all the attendant visual nuisance that implies, in particular the slight but obvious blurriness. Worse, last night I somehow managed to access higher resolutions that were properly functional - and now they're gone....

I think those properly functional extra modes appeared because I was screwing around with
Custom Resolution Utility, but now that they've disappeared they seem resolute in not being recalled. No amount of CRU jiggery-pokery nor driver replacement seems to work.
I don't know exactly what's going wrong. (1) My laptop GPU is technically capable of up to 2560 x 1600 x I-don't-know-what refresh rate, so making it run a 2560 x 1440 monitor is a stretch. (2) Unless you can patch the driver, connecting this laptop to that monitor by a single HDMI cable seems apparently to impose a 165 MHz frequency limit on what can pass through (and therefore an upper limit of resolution x refresh rate) (which actually should mean 2560 x 1440 x 44, shouldn't it?)
Anyway, some hardware constraint's making it not work in the way I dreamed it would. Let this be a lesson to you all, kids. Don't reach for the sun on a ladder of straw.