Those specs match the 172W 24V 40X40mm peltier that I'm using
.
The Maximum Ampage rating is just that, a "maximum" draw rating, so although your estimate is perfect Mat, it isn't a 280W peltier
. At 24V this peltier draws about 7.2A.
18V would be perfect for this peltier, as at maximum voltage diminishing returns start to kick in; as heat production increases it begins to outweigh the extra boost in capability that last 2-4V (~10%) gives you. I'm running mine on 22V, and it's working very nicely.
If you would like, I'll test out my setup, with the same peltier, at 18V for you, and see if there is a signifigant difference in performance compared to 22-24V.
If that variable PSU is inexpensive, I would grab it. A variable output PSU is a very useful thing to have, and you could even conceivably cool the PSU with a 24V fan or two, and run them off of the PSU itself for a really clean setup.