The good news? All of the methods worked pretty darn well, producing flavor that, while not quite perfectly fresh-tasting, was at least as intense as any herb that you've cooked in a sauce for a few minutes.
Fresh herbs are living things with active enzymes and flavor compounds that change dramatically when heated or damaged. Herbs stored in an ice cube take much longer to melt and incorporate into a sauce than herbs stored in frozen oil, which means that while you're waiting for the core of that ice cube to melt, the herbs that have already melted into the sauce are busy overcooking and losing fresh flavor.
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