Inscription - The Word of Knowledge

Question

You are part of an exploration team, and are searching around the North of Scotland, where you stumble upon a strange inscription in the wall of a cave, that is out of place in an otherwise decidedly Egyptian decorated interior. As you are the team's expert in solving such things, the team turns to you to solve it.

This here is the inscription as a whole. Deciding this is not in enough detail, you take some close up photos.

This is a photo of the main inscription, rather badly written, but hopefully still readable.

Beneath it all you notice a word: Facal

Can you work out what it all means?

Hint 1

All parts of the inscription are useful, and keep in mind where you found it.

Hint 2

Who is depicted in the top right side of the inscription?

Answer 1

The speaker (top right)

The speaker depicted in the upper right of the inscription is clearly

the Egyptian god Thoth, an ibis-headed man.

Hunting around a bit for this person in connection with ciphers or scripts, I came across

the Word of Thoth, a fictional hieroglyphic language created by fantasy author Matthew Reilly.

The best translation of this script I could find online is

the following fan-created table found here (click for full resolution version):

The main inscription (left)

Using the above script and table, the main inscription transliterates line-by-line as follows:

HTMNHHRMIISOAEH
TORUGTKTSSOUITET
THDPCOHNBARCUEH
CITTSEAPEOSEKMMT
OPINOEAIIEENEECIA
MNTTSIROTTDEOPM
RFACEIBDMHRLDNE
DWOLNTTEISSOEOC
TSLTGMCODOEUMER
MTINNGISEEFOSCNAA
TAME

Now, what should our next move be? Well, my gut feeling about the relative letter frequencies (based on typing this out letter by letter) was confirmed by checking with Rumkin:

the letter frequencies are exactly what one would expect from ordinary English. Common letters like E, T, and A turn up a lot; rarer ones like K, G, and B turn up less often; and the rarest like V and Z don't appear at all. This would be very unlikely if the letters had all been switched around by some standard cipher like Caesar, Vigenere, Atbash, or letter substitution. So we must be looking for a different sort of cipher, possibly involving a simple rearrangement of the letters.

The hexagon and arrows surrounding the inscription suggest to me that we need to do something involving

rotation and the number 6? Just for good measure (and despite the previous paragraphs), I tried Caesar-shifting by 6 characters each way, but without success. We may need to actually rotate the square of characters, but we'll need to decide on some kind of alignment for it first.

I tried splitting the ciphertext up into

groups of 6 characters and taking the final letter of each group, which started off promisingly but then faded into gibberish: HORSE CRIP MNEISDFFNNSSOENFAE. Taking the first letter of each 6-letter group gives another string which is only just over the line into unintelligibility: HRAUSTOCTEMOEAIEAMETOLDRGOT.

The shorter inscription (right)

The shorter string of characters over on the right looks like it could be something arithmetic. I'm wondering if this could be relevant, along with the operations like $+$ and $-$ and $\times$?

The word at the bottom

Looking up "facal" on the internet gave me

this Wiktionary page - apparently it's a Scots Gaelic word meaning "word", "language", "comment", or "phrase".

Given the Scottish connection in the question, this can't be a coincidence - it's not just a typo for "facial" or "faecal". Perhaps it's telling us that

Scots Gaelic

will be involved elsewhere in the solution too (which would be awesome, btw).