If we don't simply agree on the premises, an argument has to be made to support the ones we don't agree on, and that argument will have further premises. If we don't agree on those premises, an argument has to be made to support the ones we don't agree on, and that argument will have further premises.
Eventually we agree on premises, and work our way back up.
>the pure mechanistic check of the operations/conclusion part that logical fallacies provide is very nearly useless.
I think that it's the only important part of evaluating an argument. So our premises differ. If further arguments that you plan to make rest on the premise that the mechanistic checking of the chain of reasoning from premises to conclusion of an argument is very nearly useless, I may be able to recognize the soundness of this hypothetical argument, but never the validity.
> in a moral issue, the premises depend on your values, not some objectively verifiable external truth.
That I claim to have a moral value is an objectively verifiable external truth.
>On issues of personal interest, the premises depend on what benefits whom. Etc.
When?
>On political issues the nuances and justifications for the premises are so rich that it's not even worth trying...
Isn't the entire political process an act of trying?