Do you know of any specific transformers for option 1, PCB mounted?
Yes, the brand and model I mentioned. These are wound with four separate coils on dual plastic bobbins, they are not overwound with just paper layers for isolation.
Signal Flathead low profile PC mount transfomers
If you're within the USA, both DigiKey and Mouser stock this product. Several other transformer manufacturers make similar products but I'm most familiar with Signal.