Even now the surround of tthe new woofer feels much more flexible and compliant than the "good" old woofer. Maybe I should change the second original woofer, too?
Seems like a good idea to me. (Or replace the surround yourself, at least, assuming that matching replacement are available - usually a task reserved for decades-old drivers with foam surrounds.) If you're so inclined, you may want to rig up a TSP measurement setup and observe the differences. I would expect the old driver to have a higher fs and lower Qms.
I do find it disturbing that the surrounds in a name-brand driver would have degraded that much in what can't be much more than a decade, assuming the drivers weren't super old stock to begin with. The driver datasheet does mention a "natural rubber surround", and if I can tell you anything about natural rubber, it's that the stuff doesn't last and tends to go rock-hard or turn to goo after a few decades. Still, this seems a bit extreme.
Side note, the driver datasheet also mentions
Long, high temperature voice coil wound on an aluminium voice coil former gives low distortion and high power handling capacity.
High power handling, yes, but low distortion, not quite. It's a good thing that it's only being used as a woofer and crossed over around 600 Hz, as Al voice coil formers tend to result in major electrical nonlinearity and IM distortion due to eddy currents.
It may be a good idea to check the surrounds on the midranges as well, as they are of similar construction.
That, incidentally, includes the Al voice coil former. Oh crap. That's not a good design. The glass fiber variety would be much preferred. Who does that in a midrange? (Well... with fs = 68 Hz, it's arguably more of a midwoofer.) It would be salvageable with current driving, but that's not happening in an existing passive-XO design. Now again, being in a 3-way would help out quite a bit in practice, but is it ideal? No.