Each letter represents a different number from 0 to 9. Convert all the letters, solve the sum, and find the hidden word.

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What I Didn't Do

I'm not 100% sure that all of these are solvable using just logic.
I've managed them, thus far, but there's an awful lot of guesswork going in.
I might need to simplify it a bit, but I'll give it a few days before I decide for sure.