I don't know the extent of internal Spartan politics regarding the decision to only send 300. Historians blame it on the religious festival. Spartans did have a history of adhering to these religious events.
As for amphibious operations, it would have been difficult to transport the entire Persian army across to the Peloponnese, but not difficult with a modest size force. The Athenians were very successful in amphibious operations against Sparta and its allies on the Peloponnese during the Pelopensean War during the next century.
The key was that the Athenian Navy made difficult to mount such an operation.
I don't know the extent of internal Spartan politics regarding the decision to only send 300. Historians blame it on the religious festival. Spartans did have a history of adhering to these religious events.Fair enough. 'History', as it was written then, tended to gloss over those kind of internal politics in favor of the conflict without. Most historians that I have read agree with you -- that the delay, and the small size of the Spartan force destined for Thermopylae had to do with their strict observance of religious festivals.
I find that explanation unsatisfying. Still I have no evidence to the contrary, only speculation.
BTW, if the Athenian Navy was such a threat to an amphibious operation, why couldn't they have destroyed the Hellespont bridgehead just as easily? Seems to me the bridge was a fat target.