And how would it deal with more abstract forms of labour, like singing or psychology?
When we think about what society should look like, we should begin from the now, by understanding how present society works. Marx calls this scientific socialism. Utopian socialism is when we make up imaginary worlds in our mind about what society should be like and try to implement that imaginary world in reality.
So questions like these are not really useful, because the answers are contingent on so many unknown, untested factors. We can speculate some systems, but we have no idea how that system would actually work, meaning we cannot work towards that system because we don't know its actual performance.
A more useful question would be, how would we change how wages presently work to make it fairer. FWIW, Marx answered this as "to each according to their work", not "to each according to their need" which is something to implement in communism(but not socialism).
From all according to ability, to all according to need. Value assignment is not necessary, we merely only expect for workers to give it their all (which in a highly industrialized and automatized economy like ours will probably be very little). In addition, they are free to take all that they need. Food, vacation time, clothes, a house, books, computer games and so on.
In actually existing socialism, both current and historical, the value form and wage-labor had not been abolished (I'm talking about the USSR, current PRC, Vietnam, Cuba, etc). For these countries they couldn't abolish these because they hadn't accumulated enough capital/means of production to allow for the above. Instead, they'd manage a socialist accumulation of the means of production with a more equitable distribution of resources while temporarily tolerating inequality.
The USSR, for example, had employment guaranteed as a basic right and everyone received their wages if they fulfilled their labor quota - and differences in wages between engineers/psychologists/whatever and more manual labor was highly managed (I think I remember it was official policy to keep the wage ratio between 1 and 2 for any job... imagine making 75% of what a doctor makes at your retail job!) It obviously wasn't perfect because as you rose up in the party you also acquired way more better stuff, vacation time, cars, goods, etc. Yugoslavia had some kind of market socialism I'm not familiar with.
If such a system needed to be set up in the west after the revolution, we'd accomplish it broadly along the lines of the soviets. Guaranteed full employment with a wage that everyone from miner to cashier to engineer to surgeon gets plus or minus 50% - if anything, the miners should probably make more than the doctors! What would determine wages would be central planners.
To add to this, without the ability to purchase capital, property ownership being regulated, and central planning, excess wages become less and less useful. If one's material needs are met and they cannot purchase capital, what are they to do with excess wages? This is the premise for the abolition of the wage-labor relationship and eventually the transition to higher stage communism.