Do you think that this is what utilitarianism is, or ought to be?

Utilitarianism does offer the possibility of a precise, algorithmic approach to morality, but we don't have anything close to that as of now. People disagree about what "utility" is, how it should be measured, and how it should be aggregated. And of course, even if they did agree, actually performing the calculation in most realistic cases would require powers of prediction and computation well beyond our abilities.

The reason I used the phrase "artificially created", though, is that I think any attempt at systematization, utilitarianism included, will end up doing considerable violence to our moral intuitions. Our moral sensibilities are the product of a pretty hodge-podge process of evolution and cultural assimilation, so I don't think there's any reason to expect them to be neatly systematizable. One response is that the benefits of having a system (such as bias mitigation) are strong enough to justify biting the bullet, but I'm not sure that's the right way to think about morality, especially if you're a moral realist. In science, it might often be worthwhile using a simplified model even though you know there is a cost in terms of accuracy. In moral reasoning, though, it seems weird to say "I know this model doesn't always correctly distinguish right from wrong, but its simplicity and precision outweigh that cost".

So, do you think that, absent a formal algorithm, when presented with a "save" formulation, a (properly trained) philosopher should immediately detect the framing effect, recast the problem in the "die" formulation (or some alternative framing-free formulation), all before even attempting to solve the problem, to avoid anchoring and other biases?

Something like this might be useful, but I'm not at all confident it would work. Sounds like another research project for the Harvard Moral Psychology Research Lab. I'm not aware of any moral philosopher proposing something along these lines, but I'm not extremely familiar with that literature. I do philosophy of science, not moral philosophy.