All good advice thus far. You're going to learn a lot about different damping properties with some of these experiments. Far too many materials over damp, using damping is not the way to tame brightness, Brightness is symptom of something wrong upstream, usually inherent to components and/or parts within components. Need to fix this prior to damping experiments.
You're ideas about modding cd player are more on right track. Re-clocking may be problematic, likely present clock circuit won't support clock upgrade. Op amp upgrade may be beneficial, research your op amps, make sure its compatible op amp. Coupling caps good place to start. Discrete voltage regulators can be another nice upgrade. Keep in mind if you're novice, may damage cd player beyond repair if you make mistakes.
Not sure you're in position for upgrades in equipment, but that would be of greater benefit than mods. However, if you're intent on mods and learning what they can offer, you're on right track.