If I read your description correctly, the device, in pic 5, is a "choke" or inductor use to reduce the ripple in the DC output. If you look closely there is an approx 1/4" insulating board between the top lamination pack and the bottom "E " lamination pack. It has a single continuous winding, it may have several additional taps depending on the design.

I would examine the entire assembly carefully. IF one of the high current winding failed you should have little difficulty in finding the failure.

Check the control circuitry to determine if the failure was caused by a bad relay/contactor.

These old brute strength units are difficult to break unless you really try.

Many of the manuals are on the net. It is likely you can get a manual from Miller (bring clean money). The old welders in many cases had incremental changes so a before or after vintage manual will assist you in getting a schematic.

Diodes are available on Ebay. If you can find current and voltage ratings for your diodes, more E & I is good. Also Banggood & AliExpress primo chinesium products.

Good Luck

James Geraci