Wow Scrit, that is an amazing idea! Please keep working on it! I cannot believe my luck, as this is the first thread I have looked at since joining, that I have found something that I am very interested in and would like to offer my advice and give you some recommendations.
As someone who studies the Furthark, I agree that Aswynn and Thorsson are great resources that expand upon the metaphysical nature of a magical language and how it can be applied to 'real life,' which I imagine you are trying to imitate with your constructed world. Aswynn has a haunting recording of herself singing each rune, if you search for 'Aswynn Furthark' in youtube, I'm sure you'll find it. Thorsson is truly a genius and a name that can be heard in most occult circles that are familiar with the runes. In his book, "Furthark: A Handbook of Rune Magic," he goes into great detail about each rune having a specific sound, an invocation, a movement (like a martial arts).

However, in my opinion, the small amount of letters in the Furthark or your constructed language might be limiting. In the Furthark, each rune has many meanings/interpretations: a literal, a connotation, a cultural (the culture that created the runes vs the culture of the reader), a subconscious, applied to the self vs applied to a group, and the list goes on.

Therefore, interpretation must be a process and not set in stone (Think of how Lyra interpenetrates the Golden Compass, with a set of symbols but moving hands that set the relationship of those symbols)

One technique to express a desire/idea with the Furthark is to make a sigil, where several runes are placed one a top or touching another, effectively making it a unique art design. I like how you hinted at this with the "common" language.

My last recommendation, in fantasy, I have only ever seen something similar to this in "Sabriel" by Garth Nix and the table top RPG "Seven Seas" (specifically the viking people and the merchant people who inhabit the North)