In addition to things already mentioned, Spice Road Table has a hummus plate & grape leaves that are amazzzing.
QSes - MK - the aforementioned Lighthouse Sandwich. Flatbread at Pinocchio's.
EP - lots of "substantial snacks." Sunshine seasons has some good veg options. I think Electric Umbrella, too, though somehow we never manage to go in there.
DHS - this is a hard one for me. I almost always end up eating a kids meal. One of the QSes (Backlot Express?) has a veggie sandwich, but it has IIRC mushrooms & I'm allergic, so no-go. Starring Rolls, same thing.
AK - flame tree usually has a strong veggie option. They also have 2-3 food carts that have veggie options, back along the back trail.
TSes - MK - fried green tomato sandwich w/o bacon was amazing. There's another veggie sandwich, too, which I've had in the past. Chef was veg herself and lit up like a Christmas tree when I ordered - said people always overlook it as an option. LTT has some sort of vegetable sandwich. BoG - quinoa salad, French onion soup is veg (!!!) and there's a ratatouille - again, mushrooms so I can't.
Epcot - tons of stuff. Ask your server, they'll help you out. We've had some shocking successes.
DHS - Brown Derby noodle Bowl, 50s PT has veg meatballs (though I've never eaten them... pesky mushroom issue,) I've eaten at Sci Fi numerous times, a modified pasta dish I think (good, but overpriced without the meat.). Ate at Mama Melrose, it was okay.
AK - We've done Rainforest & Yak & Yeti. Y&Y has a vegetable/tofu dish that's good!
HTH!