You have a couple of problems here.

First there is the turn-on surge, which is going to be limited only by the
transformer's ability to deliver current.

Second, you're going to have a relatively low conduction angle because of
the large filter caps, which means that at N amps of output current, your
diode current will the several times N.

Third, diodes don't share current well. Putting them in parallel without a
ballasting resistor ends up with one diode having slightly lower Vf than the
other, and taking more current. The positive temp coefficient will tend to
help you here, otherwise it would go into runaway, with the hot diode taking
more current till it pops.

I'd reccomend a current probe on those diode leads, or some real power
supply design work.  Too much cap is a problem.
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