A peacock that has to struggle to survive while dragging around a conspicuous tail is clearly at a disadvantage. But if he can continue to survive, then clearly he must be pretty strong! So the peahens may choose to mate with him rather than the peacocks with less conspicuous tails, whose survival is thus a less impressive feat.

I'm not sure that's true. Wikipedia lists several competing theories:

• Sexual selection, first proposed by Darwin himself in this case: he thought peahens preferred peacocks with bigger tails, and so bigger tails evolved, regardless of expense in fitness.
• Costly signalling, proposed by Zahavi, as you describe.
• Some studies listed by Wikipedia claim that peacocks with smaller tails suffer more predation (mechanism unknown), and that females prefer males with certain tail patterns (many 'eyes') rather than size.
• Some other studies confuse everything even further by claiming big, erect, flashy tails serve to intimidate predators and evolved through ordinary natural selection.

Now, how would one test this? Especially considering that some theories mostly differ in their explanations of the evolutionary history leading to the present; they all match the present birds. I do know that real-life biologists sometime claim peacocks as archetypical evidence for sexual selection, and others claim it as evidence for costly signalling of fitness.