With a little thought...
I get the impression that only von Adler takes this thread seriously.
A couple of points - 1) The battle was lost when Hydarnes' Immortals outflanked the Hellenic position via the Anopia track and attack in Leonidas' rear. 2) It was a Hellenic force numbering between 4 and 8 thousand hoplites under the overall command of the Spartans that was conducting the defence,which was a holding action undertaken while the rest of central and southern Greece mobilised. This mobilisation was delayed by religous priorities.
Let's explore an alternative outcome in more detail.
Leonidas had posted the 1000 Phokian hoplites to protect his flank on the Anopia track - it was their home ground: there were several Phokian defensive works in the pass, one of which, the Middle Gate, had been renovated by Leonidas and was the position he chose to anchor the defence.
A small alteration would prolong the holding action - Leonidas dispatching Spartan officers to direct the Phokians. Instead of retiring to a hill thinking they were the Persian objective and being masked and bypassed, the Phokians form phalanx and dish out similar casualties to the Immortals as had already been inflicted by the main force. La Gaurde recule.
The defence is prolonged enough for the Karneia religous festival to be completed. The Spartan army would arrive at the pass 4 days later, based on their rate of march to Marathon 10 years earlier. We can expect similar deployments by the other Hellenic states as took place for the Plataea campaign the following year, with the addition, as von Adler points out, of perhaps 10,000 Thebans. There was already an advance force of 400 Thebans with Leonidas, probably the Sacred Band and auxilliaries.
Leonidas is now in a position to undertake an offensive, in restricted ground unsuitable for cavalry, with 45-50,000 hoplites. The stage is set for
a slaughter greater than Cannae, Carrhae and Adrianople; perhaps of all of them together if we take the highest reasonable estimate of Persian numbers.
What happens thereafter depends on the fate of the Hellenic fleet covering
Leonidas' flank at Artemesion. If events unfolded as OTL, they would be forced to retire. If this happens before the completion of the Karneia, landings take place behind the East Gate' Leonidas is assailed from the rear and is destroyed as OTL but leaving an even greater legend. If after the Karneia but before the arrival of the main forces, there is a chance - and I put it no more than that - of a succesful back to back defence followed by the destruction of the Persian army. More likely Leonidas is overwhelmed and 'Plataea' brought forward to that years campaign season, probably at
Chaeronea, the next choke point on Xerxes' line of advance.
Having retired down the Euboean channel in a post Karneia scenario, the Hellenic fleet would be presented with an opprtunity to hammer the Persian
fleet in restricted waters carrying out a landing. Note Leonidas will still probably be overwhelmed.
In both post Karneia scenarios I would think Xerxes, seeing the possibilty of an almighty cock up would turn over command to Mardonius and get the hell out of Dodge. This time however, minus a fleet to cover or carry him, he would have to withdraw by land to the Hellespont with Greeks, Macedonians and Thessalians rising on the news of Hellenic victories. He could well be cut down on the way.
In the instances of Leonidas being killed at the pass, history might proceed pretty much as it did. There might have been a change of monarch and revolts across the empire, but this was pretty much what happened every time there was a succession. If Leonidas and the fleet had held on until relieved and gained a massive victory? All that was holding the Greeks together was fear of Persia, the most that would have happened I think would have been a campaign or campaigns to liberate the cities of Ionia, the Greek Isles and Cyprus, after which normal service would be resumed.
Minus the Athenian Empire. The Delphic League was again a consequence of fear of Persia, that and Athenian prestige for Salamis, which of course doesn't happen. No League - no empire, No empire - no Peloponnesian War.
I think this is a long enough post. I can sketch further possibilities, but to do a proper time line justice I'll have to recall some loans and aquire more material. I have established however, I hope, that a Laconic victory is feasible with one small alteration to reality.
Cheers, this is fun.