Yes, it was surprisingly easy. We were able to secure everything we wanted, including:
Crystal Palace
Rose & Crown
Biergarten
Via Napoli
Tusker House
Jiko
Cinderella's Royal Table
Sanaa
Le Cellier
La Hacienda de San Angel
Liberty Tree Tavern (lunch on Thanksgiving)
Boma
We were also able to get a couple that we already cancelled, including Flying Fish, Akershus, Yak & Yeti and Liberty Tree Tavern for dinner on Thanksgiving (cancelled because we think the park will be mobbed and we'll want to bail).
The only one that surprised me at the ease of booking was LTT on Thanksgiving, because I figure that will be a mob scene, but we're on the front end of the 180+10 day window since we arrive on Friday.