Max size smoothing capacitor without melting the rectifier
Also, would it be safe to test the circuit without an isolating
  transformer?


You can burn your finger on a hot resistor or tear your skin on a sharp edge of a PCB. Nothing is safe; it's all a matter of reducing risk so I'd use an isolating transformer and there's no reason to believe it will saturate due to the load in fact, it'll saturate less on full load than on no-load (watch this space for anyone disagreeing!!).

The leakage inductance of the transformer windings will tend to offer a little bit of current limiting for each time the diodes re-charge the capacitor.

I will say this about the diodes - they are rated at 400V and I believe you might expect diode failure when other circuits switch in and out around where you plug this thing in - I'd go for something a bit bigger like 1N5405 (rated at 500V in reverse). I'd also ensure the cap is 450V rated for the same reasons of reliability.