There is, of course, a fairly simple alternative solution, dealing with "real" particles; the photons coming out of the filters are not the photons that went in. Photons don't travel through the sheet; the energy is absorbed, and the properties of individual components of energy determine what happens next. The properties of some chunks of energy cause similarly-propertied energy to be re-emitted on the other side. It's not that the photons have mysteriously lost the information about their "spin" in the middle sheet - it's that we're dealing with new photons with new property sets, which are being re-emitted with the emission properties of the second sheet, rather than the first.

With this interpretation, the phenomenon makes perfect sense, and the old textbooks are right - after a fashion - that the second measurement destroyed the information that the first measurement generated.