Anderton
Actually if you select Quantize Duration, note endings will quantize to the nearest rhythmic value. However, there's no way to specify "only quantize duration if the note lengthens." For example if a note is only a few ticks past an eighth note and you quantize duration to eighth notes, it will quantize to the note value it's closest to, not the next one.
Maybe
that's a feature request that should come from this discussion: Introduce the idea of Q+ or Q- to quantize dialogs where the quantization strength is not 100%. Q- would move the duration or start time toward the
previous beat while Q+ would move toward the
following beat. In my view, this would make quantizing a lot less random than it currently seems. I know that doesn't address the OP problem, but it's another thought.