Wait, you want to do a gravitational perturbation mission with 5kg, for a body of > 10^18kg? You'd have to do super duper precise measurements to notice anything (much more precise than anything we can do at the moment), and the reason we don't know the density is that we haven't done precise measurements yet.

How about just doing some more precise measurements first? I'm 99.99% certain that the high density estimate stops existing afterwards

Also, how exactly do you want to get an object without guidance or comms near enough to a main-belt asteroid?

This is all just ridiculous. Some theoretical physicist does some calculation around the Island of Stability, comes up with a high density, and tries to give his paper more relevance by finding an improbably dense astronomical object, and then wildly speculates that the two are related.

What are the chances that some rando asteroid consists of 100% of an element that we

1) don't know if it actually is stable

2) don't actually know the density of, besides a single paper about it

3) don't know any natural, plausible mechanism for synthesis

as opposed to it just being not well studied?