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Does a lot of damping material have any negative effects in a closed box?

With a steep filter of at least 24dB, most of the higher frequency resonances above 80-100 Hz, if you put the crossover point there, should be cut off. Terroretically, it should work that way, but then that so-called reality comes in, so well. It probably depends on a lot of different factors, circumstances.:)
I cross a little higher than normal, 110Hz. But power is cheap, and I never get anywhere near challenging the amp.
 
Thanks for your answers.
I took measurements between open and closed port and the differences in FR were clear. The port closed is smoother and clearly has less boost at the bottom.
There was also less jaggedness in the decay.
However, as regards the absorption of internal reflections and leakage, I believe that a more accurate measurement system and a dedicated environment are needed... that's why I'm trying to understand on a theoretical level what the story is like.

Agree with @fpitas that nearfield measures may help. You can try it with cabinet walls as well as drivers. What treatment should be applied is dependent on what frequencies are problematic. Narrowing down the sources of the resonance determines whether damping should be applied to cabinet walls or internal volume. Some experimentation is likely required. If the box is resonant, applying pipe clamps in different locations may help isolate.

Since you closed a vented box, you likely have volume to spare, so some bracing may help as well.
 
some bracing may help as well
Yes. Most speakers are built to a price. And unless the manufacturer thought bracing would sell more speakers, it was probably minimal.
 
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