It turns out that technically, the Summer Islands, Naath, and even the Basilisk Isles are not considered part of "Sothoryos" -- I mean, after all, they are islands and not "part" of the main landmass. Then again the Iron Islands aren't "part" of Mainland Westeros, but...anyway, The World of Ice and Fire treats them as very distinct, though it does group them all together in the same part of the book. The example Elyo Garcio used when I directly asked was that New Zealand isn't really "part" of Australia or any continent; is Madagascar "part" of Africa? It's an island.
To this end, the new terminology I want to introduced as a catch-all term is "Sothoryos & the isles of the Summer Sea".
There are off-shore islands which don't count under this usage because they're near to shore and tied to the mainland (i.e. Lys, the Arbor, etc.)
Great Moraq hasn't been introduced in the TV series, but even if it was we'd group it under "Islands of the Jade Sea" because its eastern shore is on that body of water, and it seems more culturally/economically linked to that region.