A Persian amphibious operation against Laconia (lower Greece) was certainly possible, but I rather doubt that it would have had much of a chance. The coastline is probably too rugged to land a sufficiently large force quickly enough to avoid annihilation on the beach. If it were so easy to do amphibious, why didn't the Great King just land his army in Attica instead of bridging the distant Hellespont? The answer is that any landing has to be far enough from the enemy's center that you, the attacker, can reinforce faster than the defender. Xerxes didn't want a repeat of Marathon.
It's the same reason Eisenhower chose Normandy rather than Calais. The flipside is that a remote landing leaves the chance that the defender can bottle-up the attacker. The Germans tried this in the hedgerows just as the Spartans attempted it at Thermypolae.
You still haven't addressed the question as to why -- if the defense of Greece was paramount -- the Spartans sent only 300? The battle was eventually lost when the Persians flanked the Spartans through an unguarded pass. Even a few hundred more troops would have greatly enhanced the chances for a full repulse. Only 300. It's a riddle wouldn't you agree?