Walk-ups are possible but unreliable. The particularly popular (like Ohana) and particularly small (like Kona) are most likely impossible. And with only 2 dinners, you can't just shrug your shoulders and try again tomorrow.
Biergarten in Epcot is a good buffet at both lunch and dinner, and often will have availability for a party of 2 because they are filling in the tables that already have groups of 5-6 (like a true biergarten, 8 people are seated at a long table. You can interact as much or as little as you want: some people chat throughout the meal while others smile, nod, and go about their business).
Just outside the Epcot International Gateway, check for openings at Captains Grill in the YC resort. Nice place, a little quieter, and for the budget they have a fixed-price option that includes app, entree, and dessert.
For your MK day - I think Tony's food is fine; if Italian appeals to you, check availabiltiy. The Plaza is another option, as is GF Cafe (quick monorail ride away). Otherwise you may have to take a bit more time from your MK day and take a bus to a less-crowded resort. Turf Club at SSR and Olivia's at OKW are 'hidden gems' with pretty good food and more availability because they are off the beaten track. Slightly closer would be to take the boat to Ft. Wilderness and eat at Trails End, a basic ribs & fried chicken buffet.