Is there any scenario, situation, or way to make "doing something selfishly" have a positive connotation?

Ayn Rand wrote a book called The Virtue of Selfishness.

As an Objectivist, she espouses rational selfishness.

That page says

In popular usage, the word “selfishness” is a synonym of evil; the image it conjures is of a murderous brute who tramples over piles of corpses to achieve his own ends, who cares for no living being and pursues nothing but the gratification of the mindless whims of any immediate moment.

Yet the exact meaning and dictionary definition of the word “selfishness” is: concern with one’s own interests.

The connotations of selfishness outweigh its denotation. To express yourself without a lot of hand-waving, try qualifying it with rational selfishness, enlightened self-interest, or simply self-interest.

I think if you use the phrase 'self-focused' you might be able to get away with it. It doesn't sound quite as bad as the other examples you have provided.

Self-preservation

Self-preservation is the first responsibility — Margaret Anderson