[wheettebott]

that all things were empty or void (sunya) of independent existence, expressed as 'own being' (sva-bhava).

Empty of "independent existence" seems to imply an interconnected existence. It is still existence or 'self', but a 'collective self', like an attached husband or wife cannot fathom life independent of their partner.

My feeling is, for the Buddha, emptiness meant when the mind really looks very acutely at something, no self can be found in there.

That is why the Buddha chose quite specific dhammas when referring to emptiness, such as the eye, ear, eye consciousness, etc.

My sense of it is his intention was for things to be examined very closely rather than Ananda's broad cosmic statement "the world is empty".

For me, the Buddha encouraged us to look very closely for the emptiness (rather than develop a cosmic theory).