I already had the 4700 µF caps available, so I measured their ESR to be about 10 mΩ. I also had a 5V, 7A transformer lying around, and I measured its winding resistance to be about 24 mΩ. That's the figure I used for my simulated transformer.
The simulated transformer ratio is such that the input is 220Vrms, and output is about 9.2Vrms. I did transient simulation with 0 initial conditions, so the initial high current surge makes sense, and the rectifier should be able to deal with it. But then, during normal operation, the total current coming out of the bridge rectifier, AM3, is peaking at 18 Amps. I measured the average of that waveform, it's about 7.57A, and the RMS of it is 11.74A.
Now I'm not sure how to rate the secondary current of the transformer ... Should I use the average current, or the RMS, or the peak 18A?