If I had an aged panel that was still working and played at a reasonable volume, I would probably just leave it alone.
There is a risk of bending a stator when prying them apart (not necessarily the kiss of death but you don't want it to happen).
Assume you would have to replace everything but the stators, and the materials, especially the 3M tape adhesives, are just stupid-expensive. Curved panels use different tape thicknesses on the front & back stators, so you would have to purchase two 36yd rolls ($200+ each). You would use about 1/3 of that tape but it's a min-buy quantity thing. Add the diaphragm film and coating will bring the cost about $500 + shipping.
You would need to build a jig (a sheet of plywood ain't cheap either).
You will need some method of determining the tension on the diaphragm and reproducing that same tension.
As for the sound:
Most panels, no matter their construction, will faithfully produce the input signal and sound about the same, as the tonal quality and response are largely determined by the electronics interface, especially the transformers.
Assuming you use similar to original materials and diaphragm tension, I wouldn't expect the panel to sound appreciably different tonally, just in volume.
If the aged panel was weak, you will hear a big difference after refurb because volume is restored and the woofer is no longer overpowering the panel.
If you substitute thinner 6-micron for the diaphragm, the treble will roll off a bit higher, which is good but you may not hear a difference if the electronics is chopping off the top octave.
If you don't get the new diaphragm at original tension, it's drum head-frequency will not match any compensating filter that ML may have in the passive crossover, in which case, you would might hear an undamped peak at the resonance frequency.
If you have a dead panel, then you have nothing to lose, and I would do a refurb without hesitation.