"Since there are “magnetically shielded” speakers on the market, there must be a way to shield them. "
Sure, with iron, and to a lesser extend with nickel or aluminum. But iron and its alloys are practically the only material used. There is a special alloy called mu metal that is used for this, for example around picture tubes, but it’s hard to buy. I think it may be better at short circuiting the last little bit of field around something sensitive than it is at shorting the intense field around a magnet.
“So, I figured a denser material would be more effective. Not so?”
Not so. It has to do with alignment of electron spin, not mass.
The effect that most materials including metals have on magnetic fields is neglible, though there are slight effects (which is why the powerful magnets in the OP can dent water, for example).