Need help debugging my project: Fuses popping like crazy, but I can't find the reason why
If you think it is happening due to inrush current, then it could probably be solved by a choke coil. They are there specifically to stop inrush current.

I would check to see if one of the diode's is fried. If you had one fried it will open-circuit for one half of the phase. When it open-circuits the coil will just become a floating load. This will cause a much higher current.

Test it by replacing the diodes. try measuring them to see if one has a higher resistance than the others.

Someone correct me if I am wrong.

Addendum:

more about choke coils.
Here are some:
http://industrial.panasonic.com/www-ctlg/ctlg/qAGL0000_WW.html
I googled choke coil to find the best explanation, I read the first paragraph of this and it sounded like it would be of help, so here you go: http://www.wisegeek.com/what-is-a-choke-coil.htm