Are there any things to consider when putting thick rubber underlayment down?
Insulate the new subfloor in the joists below to thwart any condensation issues first, as much R-value as you can get in there. Other than that no, the "underlayment approved laminate" can just sit on the underlayment &amp; you might be able to double or triple the planned underlayment, depending on the laminate manufacturer.

However, Carpet on top of carpet Padding would really be the overall best sound deadening solution &amp; your underlayment doesn't care whether it's penetrated with fasteners.