Ok. Got back to this today and things are looking pretty good. Here are my voltages with all tubes in.
Reading taken - initial build reading - current reading
B1 - 259v - 252v
B2 - 254v - 250v
B3 - 209v - 210v
PI/trem , pin 6 - 155v - 153v
PI/trem, pin 1 - 105v - 86v
Preamp, pin 6 - 142v - 159v
Preamp, pin 1 - 124v - 141v
Cathode resistor - ? - 14v
I played a little bit and everything sounds alright. The tremolo functions as it did before. I think I'm good!

Thanks so much for walking me through this trouble shooting! Now let me see if I can do a post mortem on what happened...
SUMMARYFirst the amp just died and would blow fuses immediately. Even after I removed all tubes. One of the 6K6GT power tubes i was using had a rattle in it when shook. It's a grey smoky glass so I can't see what's rattling around in there. When hooked the amp up to a current limiter with no tubes, the bulb glowed bright, indicating some kind of large current draw.
At the suggestion of shooter and PRR, I replaced the two solid state 1N4007 diodes I'm using for rectification. It should be noted that they tested fine using a multimeter (i.e. under low voltage conditions). Then we tested the power transformer and the disconnected heater string for shorts, finding none.
So we tested the voltages for the unloaded power supply using the current limiter. Voltages were high as expected for an unloaded power supply, and the current limiter bulb did not light, indicating we were ok so far.
Then we moved on to hooking up each individual section to the power supply, one at a time, checking voltages and making sure the current limiter didn't glow at each step. Once the entire supply was hooked up and proved to be ok, we scoured the amp for stray metal gremlins that might have caused a short somewhere.
Since we didn't find any, we added the first tube (preamp), and tested again. Voltages looked high for the preamp, but that made sense. Since the current limiter bulb did not light, we repeated the process with the PI tube added. Finally I powered up with the power tubes in and got good readings and the amp seems to function fine.
Did I summarize the process correctly, or miss anything?
Ok, now to the cause.
POSSIBLE CAUSEI'm guessing my 6k6gt had a catastrophic failure. Since i can't reall see what's broken, I'm guessing it was either the heater or the plate...but I don't really know. Then failing power tube drew a bunch of current quickly causing the fuse to blow.
Based on the fact that the only thing changed were the rectifier diodes, I'm guessing the current rush from the failing tube burned the diodes in such a way as to become a shorted wire under high voltage conditions, thereby basically causing a short right at the start of the power supply, before the first filter cap.
So...can all you gurus comment on whether I've correctly understood what happened and how we located the problem?
And, again...thanks to everyone on this site who helped me (and all the other folks like me on this forum)!