Enclosure Dampening

You'd need to make a heck of a difference for a change in damping to affect behaviour that much. Not absolutely impossible: for e.g. some mid-TLs are used to tailor the mechanical high pass of the driver, so a big change (it would need to be a big one) can affect that part slightly, which in turn will impact on the electrical filtering. We're talking fairly rare / extreme cases here though. What's wrong with the existing damping?
 
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Two very different aspects to address; enclosure panel secondary emission energy damping, which should not be related to speaker frequency response, and internal damping.


The latter is needed to remove internal mid energy, and prevent it from re-exiting through the cone, but if overdone can also block airflow, reducing the designed bass O/P.
Hence the tendency to place the woolly stuff around the walls, leaving a 'tunnel' for the bass resonance airflow.
 
99.99 times out of 100 true, but as I noted above, there are a handful of exceptions.

As was pointed out, bitumen is intended to add mass to panel walls, lowering their Fs; since it also lowers their Q in the process, whether this is beneficial or the reverse depends on the design. If the dacron was in there by design & there's nothing wrong with it, then there's nothing wrong with it. You can lag the walls with a suitable felt, jute carpet underlay or similar if you feel like it as well, but assuming the original design was competent, you're not likely to gain much, if anything, and it certainly will not affect the crossover.