Spending all morning on a mindless task while hopped up on ADD meds can produce all sorts of weird ideas. Like how the various Non-hermetic magic systems would look mashed together. At first I tried to imagine a single unified tradition cobbled together from large chunks of Ancient Magic, Rival Magic and HMRE. It was a bit to much, soo I came up with these...
Learned Rune Magicians
Nightwalking Amazons
Elementa-Spelli
Sahirs of Soqatran
Gruagachan Wielding the Language of Adam
Folk Fertility Witches
The Hyperborean Hymes of the Augustan Brotherhood
Okay not really all those necessarily. But rather the idea of buffing up or re-imagining non-hermetic traditions by putting two together. Mostly by trying to adapt the breakthroughs one tradition might provide Hermetics to another non-hermetic system.
It's interesting once I got home and started thumbing through my books some ideas held up really well. Like an (insert name here) Rune Magic Breakthrough is awesome for almost any tradition, particularly mathematici. Or the idea of a Folk Witch tradition with fertility magic. Or how much more powerful potential rivals like the Augustinians or the Amazons would be if they had reliable access to some version of Nightwalking.
My favorite hybrid (due to how complementary the powers are) is the Mobed-Sahir. Invocation+Adjuration for a summoning art, plus access to True Names and Divine Mysteries up the wazoo.
I am working about Breakthroughs for differents Traditions. The Folk Witch (and Hermetic) Familiar for Elementalist and Vitkir could be interesting, and that would make them more near to the Hermetic Power. The Muspelli could have Daimon Aspects like thir Familiars, like the spirits from Gruagachan.
The option to make Enchated Items of some extent with any mean for Elemntalist could be very interesting, simply with the Craft Magic (lesser maybe), and munchkin if they can obtain Vis from Refining Art.
While I was generally very pleased with HMRE, one minor complaint I had was related to the fact that most of the Virtues and Flaws made available to members of the traditions described were taken exclusively from the core book. Subsequently, I spent quite a bit of time thinking of ways of adapting V&F from TMRE and other supplements to work with various hedge traditions - most notably I wanted to use Potent Magic to circumvent the fact that Magical Focus is decidedly less impressive for traditions that utilize Difficult Arts.
Ultimately, however, I found that most Hedgies are already so focused in their areas of expertise that they fail to benefit much from the majority of virtues and aren't especially encumbered by the corresponding flaws.
Of the examples you describe above, I fail to see the advantages of 3, 4, or 7. Would you care to elaborate?
Funny that I'm re-imagining the witches from the 4e adventure Festival of the Damned using this basic concept - primarily folk witches but with a (very focused) fertility ritual.
Oh they would all be pretty awesome. Hordes of undead+hordes of elementals! Control your own spirit teachers! Augustan Brotherhood with some actual punch to it! They would all be a straight up huge increase in power. Especially the Sahir one.
That said, its totally non-thematic. For starters the Sahir and the Soqatran are totally different concepts. Sahir control spirits and Soqatran are controlled by them.
Well I tried to mention a combination for each tradition I could remember on the fly. There were reasons for each but admittedly a few are a bit tenuous. And yes mostly non-thematic.
Elementalist's + Muspelli= Elementalists able to assume giant elemental Mythic forms and perhaps spont literally earth shattering rituals.
Sahirs on Soquatran was mostly mentioned because of geography. In my mind Sahirs should be more likely then Hermetics to travel to that island. They could certainly benefit from learning the secrets of Soqatran. Improved Vis economy, greater longevity, long term bonds with spirit servants/mentors.
The Hyperborean Hymes of the Augustan Brotherhood. No great synergistic benefit but it does kinda rhyme.