Balanced to RCA

I agree that the transformer approach is superior to simple adapters, especially when going from balanced output to unbalanced input. It allows you to use the whole signal (rather than half of it) and is less likely to cause hum issues. Whether the improvement will be significant is situation dependent, but it's the best approach, IMO.
Adapters from unbal to bal sometimes ground one of the active pins (2 or 3 of XLR), but that is not advisable going from bal to unbal, as you would be grounding one output of your source component, which could damage it.

For a definitive answer, I’d go with the recommendation of the manufacturer of the balanced-output source component. (Some manufacturers even provide wiring diagrams for their recommended method of going from balanced to unbalanced.)

It makes me uneasy to short any output to ground, but I’m not an EE nor a circuit designer, so there’s a lot I don’t know.