Utilitarianism and Kantianism applied to abortion.

How can dueling definitions of "personhood" lead to an irresolvable impasse if "personhood" is irrelevant to one side's argument?

Are you suggesting that Singer's argument doesn't rest on the definition of "person?"

Now, whether Singer simply uses "person" as shorthand for "a rational entity with self-awareness" or not is largely irrelevant,

his main point is, I think, summed up in the following syllogism:

It is not wrong to kill a non-person
A fetus is not a person
Therefore, it is not wrong to kill a fetus.

Substituting "rational entity with self-awareness" for "person" in the foregoing syllogism doesn't change the conclusion, which is that it is not wrong to kill a fetus because it does not share the same status with most other entities that we commonly refer to as "persons."

I suspect that in the future, things that we "know" about self awareness may change dramatically.

And exactly how much neurological activity makes one "self-aware"?

Is an elephant self-aware? A horse? A dog? A mouse?

Perhaps we should label all of our steaks "soylent green" since cows might be "people".

I'm unfamiliar with the term "soylent green".

Soylent Green is a 1973 science fiction movie depicting a dystopian future in which overpopulation leads to depleted resources, which in turn leads to widespread unemployment and poverty. Real fruit, vegetables and meat are rare, expensive commodities, and much of the population survives on processed food rations, including "soylent green" wafers.

if it involves that we reconsider our self-righteous prejudices against cannibals, perhaps we should do that, too.

Hence, to a pro-lifer who accepts Singer's usage of the word "person", the disagreement revolves about features of the embryo that can, at least in significant part, be tested for empirically.

And the pro-lifer who rejects Singer's usage of the word "person", their disagreement would revolve about three things:

1. empirical disagreements about the subset between [X] and "rationality and self-awareness" and [X],
   
2. any subset of [X] that is not contained in "rationality and self-awareness", and their disagreement about its relevance, and
   
3. any subset of "rationality and self-awareness" that isn't contained in [X], and their disagreement on whether it's relevant

Either way, there need not be any talk about lofty persons of "personhood". Only about concrete features that the disagreeing parties consider relevant.

If the parties want to frame that as a dispute over whether that category should be called "rational beings who possess self-awareness" or "persons" is just a matter of semantics.

It may, but the majority of abortions are performed for other reasons.