Firstly, I thought we were just appealing to consequentialism, not utilitarianism?

So I think I agree with you that believing you have a utility function if you in fact don't might suck, and that baseline humans in fact don't. I was trying to distinguish that from:

a) believing one ought to have a utility function, in which case I might seek to self-modify appropriately if it became possible; so something a bit stronger than the "pretending" you suggested.
b) believing one should strive to act as if one did, while knowing that I'll fall short because I don't.

The second you addressed by saying

I would suggest that trying to achieve an actually impossible moral code, let alone advocating it, is basically unhealthy.

Did you have the same position re. Trying to Try?

I have one group of intuitions here that claim impossibility in a moral code is a feature, not a bug, because it helps avoid deluding youself that you've finished the job and are now perfect; and why would I expect the right action to be healthy anyway? But this seems like a line of thinking that is specific to coping with being an inconsistent human, in the absence of an engineering fix for that.