Given that, what does it mean when I say "I think we should express 'action A increases the value of utility function U' in math as X", which seems like a sensible statement?

I think it makes sense as a statement about decision theories. How would a choice of which mathematical expression of 'action A increases the value of utility function U' affect actual utility? Only by affecting which actions are chosen; in other words by selecting a particular (class of) decision theory which maximizes utility due in part to its expression of what "should" means mathematically.