Hi there, I used to be a pretty picky eater too. Many of the restaurants will have at least one dish for picky eaters.... a lot of the places like to do goofy things with your steak or chicken, like pile it on top of a huge icky mushroom or some asparagus

but you can request to not have those if you don't like them, or just remove them yourself which is what I do.
Now here are some of my recommendations
At the MK: Tony's (you can get just regular spaghetti)
MGM: Mama Melrose (if you like pizza, theirs is VERY good, don't be scared by looking at their menu)
Epcot: LeCellier in Canada has great steaks, cheese soup, and yummy breadsticks and none of that came with anything gross when we ate there.
If you want to be a little adventurous, but not too much, if you like Mexican food, I'd suggest San Angel Inn.
Downtown Disney: House Of Blues is excellent and you can get steak there, among other things. You already mentioned Planet Hollywood, which is a great place to go for lunch because they are not crowded then.
Now our all time favorite place to eat is O'Hana at the Polynesian Resort. The food there was out of this world and not scary at all, AND all you can eat. My fiancee and I went there last trip on a really busy night, without a Priority Seating... had a short wait and were given a table that had a direct view of the castle across the lagoon. It made a fun "out of parks" night and after we ate we explored the Polyn., Contemporary, and Grand Floridian.
Have a good time! I highly recommend checking out the menus from Deb Wil's website whenplanning your trip, and most places have the menus posted so you can check it out when you're there, too, to make sure there is one or two entrees you'll like.