Morten St George Theory

[nablator]

There is reason to believe that the cones were there in the early 13th century:

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I will admit,however, that Voillet's cones look a little nicer!

You are right about these towers at the main entrance. When I visited Carcassonne the guide told us that some roofs were added by Violet-le-Duc ; she must have meant some other towers and/or battlements. For these three towers, the roofing material was changed from slate to tile in 1960 because of the controversy, but slate may have been used in some places because northerners were involved in the construction.
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More shallow pitch terracotta tile roofs, typical of the south of France, probably covered towers at Montségur II:

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and Montségur III:

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There were apparently no battlements anywhere in France with merlons shaped like sparrow tails. Just google merlons + "queue d'hirondelle"... only northern Italy and Tyrol come up.

For the "keys" in the First Folio there are pages on your web site that I missed, I will read them this week. In You are not allowed to view links. Register or Login to view. I am surprised by:

Geoffrey (who wrote in Latin) was looking at the original manuscript of those prophecies which were likely written in Latin.

From a quick browsing of books on the subject I see that Geoffrey of Monmouth is said to have translated the prophecies from Breton. Some older sources are referenced but I have not found any transcript or translation yet.