I doubt it's Romantic myths since people that come to my mind mostly lived in the XX century

The Romantics invented the myth of insane geniuses touched by divinity, but that doesn't mean people holding that belief suffer from amnesia and are unable to list any examples from after the Romantics... Given the lifetime prevalence of any mental illness in the general population, it would be surprising if one couldn't list some anecdotes like Godel.

That's the point of experimenting :-)

There's a practically infinite number of genetic changes one could make. Understanding of genetic networks influencing cognition will have to be extraordinarily good before any researchers can write down a completely novel gene or variant which has no natural examples and experiment with it. For better or worse, for the next several decades, we're stuck exploiting natural variants - all interventions are going to look something like 'people with X seem to be smarter, let's try adding X to others or select for it' or 'Y is a rare or de novo variant, maybe it's harmful, let's remove it or select against'.

Though dog breeds are widely considered to vary in intelligence -- have there been any attempts to quantify it?

Yes; take a look at this, and the generic wikipedia page. One of the more visible tests is the number of times a new command must be repeated to be learned. Overall, there's not too much agreement because there are a number of different interpretations of what it means for a dog to be intelligent, and no one has (to my knowledge) done the factor analysis to look for g in dogs.