Yet Another Possibility........

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Sister the new joists right alongside of the existing ones. Make the new joists shorter (lenghwise) than the old, so you don't have to fit them into the old cavities. This way the very ends of the old joists are carrying the load for both, but this is not a problem unless the old ends are rotted. I am talking about the new joists being 6 to 8 inches shorter than the old.
This way, you will double the bending strength of the old joists.
Good Luck!
Dodgeman