I'm in a somehat similar situation now, except I'm considering going through a power supply that still works to keep it from failing in the first place. At the very least I'll replace all electrolytic caps except for any on the primary (usually a 47 µF/400 V) but I'll try to find out if there's anything else likely to fail in a catastrophic manner.
As long as you're aware of the fact that those primary capacitors can hold a potentially deadly charge for a long time I can't see how you could damage a power supply any further (I'd suggest bleeding the cap via a 100 kΩ resistor) but depending on how much you know about diagnosing power supplies you might end up replacing a lot of stuff without actually fixing anything. From your questions I guess you don't really know more than I do and unfortunately that's very little. I recently tried to do a - fairly straightforward - Amiga 500 power supply and after having replaced all electrolytic caps, the fuse and a physically broken resistor I still haven't gotten anywhere. I suppose the next step would be measuring output voltages and trying to determine if the switching circuit does anything at all and if it does, which voltage is affected. Without schematics and intimate knowledge of the workings of a power supply in general I'm afraid it'd still be hard to figure out which parts do what and are likely culprits.
By now there isn't much left of that Amiga brick so I might get it done - basically I'm down to something like five small transistors, two voltage regulators (probably one for 5 and 12 V each, haven't bothered to check the numbers, just saw they started with LM), a thyristor and two parts I haven't been able to identify because they're in such crowded places I can't read anything on them. That's seven parts, probably a few cents each so I suppose in theory I could just replace all of them - in a worst-case scenario only to find out that the transformer is blown open.
The MDD power supply is considerably more complex IIRC so there might be a lot more that could fail. If I find out any details I'll let you know!