In my reading, injera is a sourdough-leavened flatbread, and it does indeed have the consistency you describe. I've made it with wheat and (the more traditional) teff flour. It's not sweet or quick-bread (in any sense!) but is fun, tasty, and worth a try to eat or make.
If I'm understanding correctly, what you're looking for is a pancake with qualities I'm often trying to avoid. :) Guesses on how to get where you want, based on what you've got so far, based on what I've done accidentally in the past. Apologies that this is all over the map.
- Over-mix your batter. With quick-breads you often want delicate crumb; over-mixing will give you more gluten development (assuming wheat or other gluten-containing flour). This will have a more rubbery mouthfeel.
- Let your batter rest longer. This will also allow gluten to develop (and/or relax), which might have a similar effect.
- Use a harder (higher-percentage gluten) wheat flour. Flours will vary greatly in protein; try a high protein "bread flour" made with hard wheat.
These might help with the sponginess factor also.
Might also want to experiment with type and amount of leavening.
- more or less quantity of baking powder, or perhaps baking soda optionally with some kind of acid (e.g., buttermilk).
- yeasted pancakes! I can't immediately find a passable recipe link, but James Beard had a lovely (albeit a bit finicky) overnight yeast pancake recipe. Give it about 4 attempts before you abandon it. :)
- Try soy milk. Unlikely to be how your favorite restaurant is accomplishing it's feat, but this might do something different because of protein or perhaps if there's other adulterants or thickeners like gums or so.
- Go off the deep end: try a thickener like corn starch, arrowroot, carrageenan, xanthan gum, ...
- Try a gluten-free pancake recipe or mix. Who knows!
Good luck! Have fun! And let me know if I've missed your goal.