Rectifier for two phases (220 V 50 Hz)
You're almost there, but not quite thinking about the problem enough in a generalized way.

If you have N leads with arbitrary AC voltage between them, then you need 2N diodes to make a full wave rectifier.  Each lead is connected to one diode going to the positive DC output, and one diode coming from the negative DC output.

Note that your bottom circuit is like that, only that you've drawn it to make it not immediately obvious.

Here is a generalized full wave rectifier for N AC inputs:



You have 3 AC inputs.  Your mental block seems to be thinking about the neutral line as special in that regard.  It's no worse than just another AC input line, so you can make a full wave rectifier with 3 pairs of diodes.

Rectifying two of three AC phases and neutral is a odd thing to do, but is no special case for the general circuit above.  Here is a plot of the voltages:



This example uses 120 V AC at 60 Hz and assumes ideal diodes.

The rectifier output is the greatest difference between any two AC inputs at any one instance.  To make this easier to see, the max of all the AC inputs is shown in red, and the min in blue.  The resulting difference is the green trace, which is the instantaneous output of the rectifier.  This is the voltage the cap smoothes out, and is what you'd get if there was no cap and you put a small resistive load on the output.

Note that the green trace is NOT relative to the same reference as the AC inputs.  It is showing the DC output when that is taken in isolation.  The individual DC outputs with respect to the same reference as the AC voltages are the red and blue traces.

For contrast, here is what full 3 phase rectification looks like:



Note that this has much less ripple, and that ripple is at 6x of the AC frequency.  Your two out of three phase rectification results in ripple at only 2x the AC frequency.