Your question relates to the value of one life over another and a God that would value each life equally would judge it on that basis.

Kill one to save three looks like a nice trade off to begin with but if the 3 just so happen to be ex-murderers then it doesn’t make sense.

You could flip it the other way round too it all comes down to each persons worth and value.

I don't think a God cares who dies if whoever dies merely is reborn as something else.
Matter and energy don't just disappear into nothingness. They get recycled.

Identity (memory and unique relationship to everything else) is lost. That is not to say that the capacity to become another living being (matter and energy) is lost.

RogueAI,

By “incremental morality,” do you mean something like the following?

• Sacrifice sick eighty-year-old Joe so that infant Pete can live. Good.
• Sacrifice sick eighty-year-old Joe so that infant Pete can avoid years of severe torture which will leave him alive but permanently damaged physical and mentally. Good, probably.
• Sacrifice sick eighty-year-old Joe so that infant Pete can avoid a few days in the hospital with Covid which will leave him permanently disabled in some not-too-serious way. Good or bad?
• Sacrifice sick eighty-year-old Joe so that Pete can have a fun 1st birthday party. Bad, definitely.

Somewhere along the line as the consequences to infant Pete become less serious, sacrificing Joe flips from good to bad. But exactly where does it flip? It seems like your OP is related to the sorites paradox.

What if no human has more or less value to the god than any other human life, or any other life, or any life at all? You can't know. What if the god doesn't think in terms of bargains, but of souls (essence, spirit, selfness, atma - whatever you like to call the kernel of a unique being)?
Until you make the decision to weigh one life against another, the situation is not within your control: you are merely a witness, a bystander.
When you make the decision which life to sacrifice, and for what reason, you do three things: take on the prerogative of a god, place other lives in a scale of your own valuation and assume responsibility for a death.
The decision alters the configuration of your soul. Do you then become more or less valuable to the god?

Let's assume a traditional all-poweful/good/knowing God exists. — RogueAI

Or we could just decide that this imaginary god has never existed and any trolly problem style scenario's/dilemmas, are ALL OURS and ANY individual faced with such a dilemma, will simply have to make a decision, and act as they decide to act, and explain it afterwards.
Dilemmas happen in everyday REAL human lives, all over this planet. The acts of the people involved will have their supporters and dissenters, and everyone who learns of the story, will have something else to gossip about.
No freaking scapegoat god is required to take responsibility from us! it's Just us humans! it's up to us! WE make the decisions about what to do when universal happenstance dilemmas or deliberately created dilemmas, come our way. Sometime there is very little or no choice at all, involved, but no matter, it's all part of our lives.
If god existed then sure, it would be a great scapegoat, but then we will forever be a baby species that remains unable to ever grow up!

RogueAI,

By “incremental morality,” do you mean something like the following?

• Sacrifice sick eighty-year-old Joe so that infant Pete can live. Good.
• Sacrifice sick eighty-year-old Joe so that infant Pete can avoid years of severe torture which will leave him alive but permanently damaged physical and mentally. Good, probably.
• Sacrifice sick eighty-year-old Joe so that infant Pete can avoid a few days in the hospital with Covid which will leave him permanently disabled in some not-too-serious way. Good or bad?
• Sacrifice sick eighty-year-old Joe so that Pete can have a fun 1st birthday party. Bad, definitely.

Somewhere along the line as the consequences to infant Pete become less serious, sacrificing Joe flips from good to bad. But exactly where does it flip? It seems like your OP is related to the sorites paradox. — Art48

Very much so! And there's no need to invoke God. My question works equally well with an omnibenevolent machine. If the machine says it's OK to sacrifice Joe to save infant Pete (or some other borderline case), what would the machine's reasoning be? Wouldn't it have to be consequantialist?

My question works equally well with an omnibenevolent machine. — RogueAI

No, that would make it a completely different problem. Machines, however omni and benevolent they eventually become, began their evolution from adding machines made by humans to count relative values set by humans. (Gods had and have a quite different function, a quite different etiology.)
Its reasoning would probably be stated in terms of benefit to the human society: calculated as useful hours of future/expected contribution per unit.

But suppose we looked at a middling case of Trolley Car, where the answer was not so easy, and said to this god: Now, earlier, you said it was OK to sacrifice one chimp and and two homeless people for two scientists and three business innovators on the cusp of discovery. What if two puppies and a grandma-in-a-rocking-chair are on the track and there's the London Symphony orchestra in the trolley? What then??? — RogueAI

I would imagine such a God would understand that many hypotheticals never come to be actual real life dilemmas. Thank god for that! And secondly that imagination can complexify simple life matters to any nth degree of convolution.

I would imagine such a God would instead ask either a). Who set up this imaginary trolley problem in the first place? And why? And what have they omitted to create this perfectly impossible scenario.

Or would ask "who set up/contributed to this actual real life trolley problem? And why? ?"

In the case of a hypothetical. No one is at fault in any answer because imagination regarding fictional events has no culpability. No one is harmed.

And in the case of a real life scenario, it is unlikely to ever get that complicated. And usually fault is shared by numerous parties that lead to the trolley running uncontrollably into the victims, for lack of foresight/critical thinking of the designers, engineers, controllers and victims to avoid the situation in the first place.

When focusing on the choice of who lives or who dies - a binary choice, we invariably omit all the choices that lead to/reduced to this in the first place. All the possible moments in which such an impossible choice could be avoided /never come to fruition. To not observe/acknowledge the warning signs/red flags/predictors of such an event unfolding.

Hindsight is 20/20. Foresight can be 20/20 if rigorous and thorough enough. Failing to be appropriately rigorous to match the destructive capabilities/potential of a device/invention/machine is called "negligence".

The best example of negligence is creating the atomic bomb. Great power. Only one way to release it. And only one result, a bad one. This is the real trolley problem. And the answer is quite simple. Don't. In the first place.

A perfect storm or poor choices is due to compounding failures by the many involved.

A benevolent God would not be involved in this outcome. They would simply point out the flaw in the argument in the first place. That the "problem" is not actually a problem at all. Just a carefully curated set of highly defined and rigid circumstances that restricts one from any alternative options other than a horrific choice to be made.

Such horrific moral dilemmas/ choices are the design of psychopathic nature. Where people are forced into conditions completely predefined in which no outcome is satisfactory. Real life does not operate in the same way, as choices are not isolated in nature but rather a continuum. And if one does create this scenario, the only person at fault would be the one that orchestrated that limited choice.