The most appropriate synonym for "sporadic" in the given sentence is "occasional." "Sporadic" means occurring at irregular intervals or scattered instances, and "occasional" reflects a similar idea of happening from time to time without regularity. The other options, such as "continuous," "indirect," and "repetitive," have different meanings and do not capture the irregular and infrequent nature conveyed by "sporadic."

The term "heralded" means to announce or proclaim something, often with enthusiasm or as a sign of the beginning of an event or a significant development. Among the given options, "proclaimed" best expresses the meaning of "heralded."

The term "invariable" refers to something that does not vary or change. Among the provided options, "constant" best expresses the meaning of "invariable," indicating a state of consistency and lack of variation.

The term "dulcet" is used to describe something that is sweet, soothing, or melodious, especially when referring to sounds or tones. Among the provided options, "sweet" best expresses the meaning of "dulcet," indicating a pleasant and harmonious quality.

The word "grandeur" refers to the quality or state of being grand, impressive, or magnificent, often in terms of beauty or scale. Among the given options, "magnificence" best expresses the meaning of "grandeur" as it signifies a quality of greatness, splendor, or impressive appearance.