No one has addressed the specific condition.
Your at a protected anchorage. There is no danger of large continuous waves.
On occasion a single 1 foot roller comes in caused by the wake of of boat.
In this specific case would some extra weight in the rigging have the effect of damping the sloshing?
Any natural motion would have the probability of causing the boat to oscillate so weight aloft would only help for the first couple of seconds then would cause even worse oscillation.
But with a single wave caused by a boat wake, what do you think?
I haven't done the math, but I can tell you that riding on a mooring with no mast is much worse than with a mast--the frequency of the roll is much higher, and so is the acceleration in response to a boat wake--enough to slide the coffee cups off the table. Seasickness is a strong function of frequency of oscillation, and it is one of the common complications of dismasting at sea.
I also think that the most common stability scenario is the dynamic response to being hit by a breaking wave from the side, where the taller and heavier masts give a distinct advantage. At one point I contemplated going to a carbon fiber mast, but the disadvantages at anchor and in storms made me decide to stick with the heavier aluminum.