[Zeppelin Mysteries Hosted by Steve A. Jones]

I thought the fantasy sequences were shot in the autumn of 1973 before Joe Massot was kicked off the project....

You're probably right. Reading Brad Tolinski's Guitar World interviews seems to indicate that Massot was still on when those were filmed. Furthermore, Jimmy claims "We shot it [the Hermit scene] in December..." Highly unlikely that it would have been December 1974, since he was recording and producing Physical Graffiti at that time, and preparing for the American tour which started in January '75. Zeppelin were 100% focused at those times, and wouldn't be messing around with that silly movie.

[Zeppelin Mysteries Hosted by Steve A. Jones]

Ever since 1970, it has been known that a majority of the tracks from Led Zeppelin III were recorded at Headley Grange, as per the original liners. Now, with the release of the Super Deluxe Edition, the accompanying book said that a majority of the tracks were recorded at Olympic Sound Studios.

Which is correct??????

I fear you are confused. III was recorded in Olympic, correct. The fourth album was the one rehearsed and recorded in part in Headley Grange (along with Island Studios).

You may be thinking of Bron-Yr-Aur, with regards to III. Nothing was recorded there; rather, it spurred inspiration, as songs were partially written there by Jimmy and Robert.