I bought my Accent used and changed (not power flushed) my ATF at 135k. I don't know if it was ever changed, and it was brownish black, not red like it should've been. And I've seen no ill effects in the last 10k miles. I didn't use Hyundai SP-III oil either. I used Castrol ATF high mileage.
Third gear getting stuck could be something more serious. Try a drain and fill. If it doesn't work you're not out that much.
There's never enough time to do it right, but there's always enough time to do it over.
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