I had not heard of Vienna bridge rectifiers until I googled them. Very interesting. Active rectification crossed with SMPS tech. Very cool. Looking at needing 60A @ 70VDC peak. Much lower currents most of the time.
SceneryDriver
You may also want to consider a switched mode power supply. They are usually more complex, and normally include an inductor, but they are typically more efficient and they reduce the input current spikes.
With a rectifier circuit, input current only flows when the input voltage is higher than the output voltage across the capacitor. In the case of a simple half wave rectifier, the input current may only flow for a few milliseconds, but it must charge the capacitor enough to sustain the load current for the rest of the cycle. That means the peak input current may be several times the output current. As the output capacitor is increased in size, the output voltage doesn't droop as much, and the capacitor charging time actually becomes shorter, resulting in higher input current spikes.
Of course, using a bridge rectifier, or a three phase input, or almost any of the more complex circuits adds more diodes to conduct, and more conduction time. So these all lower the input current spikes. But if you don't calculate the spike peak current, there is a good chance you are going to kill the diodes or something else in the circuit.
Switched mode power supplies can also reduce the input current spikes.