I agree with Kari. I've definitely been rushed thru quite a few meals at WDW - especially buffets; but I've had wait-staff try to clear dishes from the table before I've finished with them at some TS as well (Sci-Fi, MM, RFC, 50's PT, & LTT come to mind.)
Don't know what restaurants you're planning to dine in, but if they're buffets such as CM, CRT, TH, CP, etc - be prepared to feel rushed, especially at such a busy time.
If you're dining at a Signature such as CG, AP, Yachtsman's, Narcoosee's, FFC, or Jiko, you'll be fine if you do as Kari suggested and order each course as you progress through your meal. You'll be asked to inform your server of your choice of app, entrée, & usually dessert upon being seated & briefly looking over the menu; but you can politely let him or her know that you'll be ordering as you go along. Kevin had a Podcast segment regarding this very subject & how he dealt with it at one of the restaurants he reviewed, but I don't remember which one. Will see if I can find it.
If you're eating at LC, CR, or TTS be prepared for the Bum's Rush! Just remember that you're paying a pretty penny for your meal and feel free to eat at your own pace. You're not obligated to rush because your server wants to turn the table over (& maximize tips), nor are you to blame for the restaurant's policy of overbooking "reservations". I realize that just saying that doesn't make it any easier to relax in a hurried atmosphere tho...
Even tho I agree it's difficult to relax when there's a line at the check-in podium, please try to blissfully ignore it - especially considering the price you're paying.
I've found that some resort venues generally offer a much more leisurely pace - GFC, Sanaa, Turf Club Bar, & Captains Grille were especially relaxing. They are however, off the beaten path, and might be busier than usual at Easter time. And I have to say that the Cape May Café Buffet Breakfast was & is one of our favorites - both for the food & lack of chaos/cacophony.
YMMV, but HTH.
Bon Appetite!