hi Dr22,
The 10VA txr will not be able to maintain 19V-2*V diode drops at 550mA.
The 19V -1.4V = 17.6 is the Vpeak you could expect when the load current is close to zero, at 550mA I would expect the input to the LM317 to ~15.5V
The 470uF IMO should be increased to 680uF or 1000uF at 25Vwkg.
You will need a h/s for the LM317, a black finned type about 3cm square, with central mounting tab for the fixing screw.
If you have the regulator project in a metal enclosure , you could mount the LM317 onto the enclosure for the h/s.