When using an amulet as one's holy symbol, does it have to take the precise form dictated by the religion (e.g., as in the table of deities in the PHB, pages 294–6), or can a player use creative license in defining the holy symbol's physical appearance, provided it fits the thematic constraints placed on it by the deity (obviously, a holy symbol for Bahamut will be some sort of draconic image)?
The holy symbol can be any symbol representing your deity. The symbols listed in the Appendix are just the most commonly used ones. From the PHB, page 151:
Holy Symbol. A holy symbol is a representation of a god or pantheon. It might an amulet depicting a symbol representing a deity, the same symbol carefully engraved or inlaid as an emblem on a shield, or a tiny box holding a fragment of a sacred relic. Appendix B lists the symbols commonly associated with many gods in the multiverse.
Note that (as always) it's up to your DM to allow or disallow any symbol you wish to use. I can't think of any circumstances in which a DM would ban a symbol, but the decision of whether a given symbol represents a deity is ultimately up to them.