Chubbycheeks,
It almost sounds like you may have figured out a few of the possible causes of yor fish passing, i.e. ....changing all of the gravel, high ammonia levels, and possibly the new fish. Which fish passed? The oranda or the other fish?It could be possible that one had an internal infection(I don't think the white spots were the cause, that to me sounds like wen growth...especially if they disappear within a few days. I have one oranda this is VERY noticable on, and I freaked out when I first saw it.....I thought it was ich!...but 2-3 days later they were gone, and the wen began to increse in size), but honestly I have to go with the re-cycling of the tank and the stressing caused on your little fish.
I too, have tried to change all of my gravel before in the past, and thankgoodness I have two very hardy ryukins that could withstand all of that re-cycling stress and the high ammonia spike. (i'm glad I too know better now!)Sometimes you get lucky in these situations, but it's generaly not the best thing to do, as I am sure you know now.
As far as bringing another fish home, it is usually wise to put them in a "quarentine/holding" tank until you sure that all things are in the green light. Even your most trusted fish store can get a fish from time to time that has finrot or ich,(if it's a wise fish store, they don't sell the fish to the public until the animal(s) have been treated

)
How is your other fish handling things?
If all goes well with the re-cycling of the tank, your other guy should pull through. Is your ammonia still high? I would recommend water changes to help aid the lowering of the ammonia(I'm trying to find a post for you on the frequency of water changes with high ammonia levels, but not having luck yet), or there is a product on the market called "Ammo Lock" It is suppose to change the ammonia to were it would be "safe" for you fish to live in, however if my understanding is correct about this product, you can still read ammonia levels in the tank after you have added the product.(Does anyone else have any information on this product?)
If you do water changes, don't vaccum the gravel for now..this also goes into the "good bug living headquartes" thing,

which is what your trying to rebuild.
Good luck, let us know how everything turns out and by all means if you have anymore questions feel free to ask!