There are TONS of healthy options nowadays.
In HS:
ABC Commissary has a Mediterranean salad with chicken that gets great reviews (skip pita chips if gluten is an issue)
backlot express: asian chicken salad or caprese sandwich, discard bread, side of carrots
Catalina Eddie's: caesar salad with chicken
Fairfax Fare: 7 layer rice bowl with pulled pork OR grilled chicken or southwest type salad with pulled pork OR fajitas, just skip tortillas (pretty sure rice and corn are gluten free)
PizzeRizzo: antipasto salad
in MK:
Columbia Harbor House has the broccoli peppercorn salad with chicken, veggie chili, salmon with steamed veggies and couscous (if that will be a gluten issue you can get double steamed veggies)
Cosmic Ray's has a half rotisserie chicken with green beans and mashed potatoes, Grilled chicken club (discard bread) with green beans, greek salad with chicken
Pecos Bills has fajitas (discard tortillas), southwest salad with chicken or spicy beef, veggie rice bowl
Pinocchio Village Haus has caesar salad with chicken and the tomato basil soup for a snack credit is supposed to be quite good there too
Casey's Corner: not really healthy but doesn't hit any of your issues you listed, featured bratwurst with caramelized onions and whole grain mustard, served with apple slices (discard roll)
Be our Guest (lunchtime ONLY): Braised pork, Nicoise salad, quinoa cakes
also consider BoG for great use of a breakfast credit and PPO positioning for 7DMT
in AK:
MANY things in Satu'li Canteen, with all the combos you can eat there many times and not eat the same thing
flame tree bbq: you can probably eat almost everything here too, it comes with baked beans and cole slaw... but they also have two kinds of salad as well if bbq sauce is too high sugar for you.
Harambe Market: grilled chicken skewer, chicken tikka masala (skip flatbread), Grilled vegetable stack
Pizzafari: caesar salad with shrimp or chicken (more an option if others in your party want to go there)
in Epcot:
Sunshine seasons, many options, all of the grill shop entrees are good, and there is a "soup and salad" shop as well
Katsura Grill (Japan): teriyaki various stuff or garlic shrimp with rice and veggies, sushi
La Cantina de San Angel (Mexico): Tacos (on homemade corn tortillas, they look soft in the pictures not fried), Pollo Cascabel (chicken, rice, beans etc)
Le Halles Boulangerie (France): nicoise salad
Tangierine Cafe (Morocco): Shawarma platters, skip the bread and couscous if you need to, the platters are huge and you won't miss them. Also chicken with saffron rice
if you can handle the sugar in it for a treat most of the hand scooped ice cream shops in the parks have non dairy icecream.
you don't have to bring food. If you can't find healthy options you just aren't looking! Also yes, planning takes time and can be "tedious" however your vacation and health are worth it. My son is picky so I have to deal with his stuff and my own, I pore over every menu and become familiar with what is everywhere and BOTH of us have a great time and eat great food when we are there even with vastly different tastes and needs.