wondering if my design is strong/structurally sound enough
A torsion box is obviously very stiff and stable, and this would make for a very very strong table just as it does with workbenches constructed this way.
But it's complete overkill for the kinds of loads a normal table would require, think about the much sparer structure of a standard 7' (2.13m) dining table which are often capable of taking the full weight of an adult. And anyway torsion-box construction is best suited to tops made from plywood or another manmade board where they can be rigidly joined throughout.
Even on a table of this kind all you should need is three or four 'stringers', one between each pair of legs and one or two in the middle somewhere. And it is directly from these that you can attach the tabletop, no need for extra battens.
The best options for attaching the tabletop to the apron IMO are with hardwood buttons or expansion plates, as shown in this previous Answer. Even on a table of this size you shouldn't need more than eight (two per side). But you could add a third along the long sides if you feel the need, it won't harm the structure in any way if you use more than are strictly necessary.
I would suggest you alter the design in another key way as well, to make the structure underneath distinctly narrower than the top, so that it has the common overhang that tabletops have. If you make any sort of apron or under-frame flush with the sides of the tabletop itself at certain times of the year when conditions are exactly right it will be dead flush as when it was made. But it could be slightly narrower during the wet season when the top expands, and most importantly slightly wider during the dry season when the top shrinks, which will look very strange!
do you think in general this will be a ...wobble-free table
That's entirely down to how flat the floor is and how accurately the legs are cut to length :-)
Any four-legged table will be stable and free from wobble if those conditions are met.