Well, that didn't last long. My new (and admittedly, budget) plunge saw
arrived and seemed perfectly well made and robust. I charged the battery
and tried a few test cuts on scrap to get the feel of the tool, then with a
deep breath decided to tackle the broken plank.

I almost finished one complete lengthwise cut when the saw stopped: it
didn't have enough power to get through the laminate. The battery indicator
wasn't at empty but neither was it at full, so I charged it again. The next
cut managed about three inches before the saw stopped for a second time.

Back to the charger. The charging light flashed once and then remained
resolutely off. So - a faulty Lithium-ion battery? Whether that's it or
not, it has to go back.

I suppose "buy locally" is the moral.