I planned my last trip with barely 2 weeks notice and was able to find dining - including Cinderella's Royal Table (I went the first week of March). And I am planning a trip next month with less than 3 weeks notice.
Here's some other things I've done (I've been 3 times post-Covid and am planning my 4th):
--Rather than stress yourself out, check a couple of times a day for updated availability. People are ALWAYS shifting their plans around and reservations pop up. I usually check first thing in the morning and then again later in the day. By defining set times for checking, you can help reduce your anxiety.
--Be sure and check for party of 4 rather than 3. And also try for party of 5 or 6.
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-Grab reservations that are available in the park you'll be going to even if it isn't an ideal time or the exact restaurant you want. Then, go in try modifying it for a better time (For example, I was able to snag a 2:30 reservation at Chefs de France in April for 4 last Tuesday when I found my trip was a "Go"- and today was finally able to modify it to 4 PM instead). And, at first I was only able to get Mama Melrose in HS for lunch, but a Prime Time Cafe opened up (which I prefer) so I switched it.
--If they add hours (which they typically do on Fridays anywhere from 2 to 4 weeks out), they will eventually add more dining reservations for those additional hours (usually by Monday or so the following week after the hours have been added). This is a GREAT time to find reservations, especially for CRT and BOG as they will be those prime end of park dining where you get to walk out of an almost empty MK AND people that have earlier reservations for those spots may change to later reservations which opens those up.
Subscribe to the "May Thread" here and someone will surely note if times are added.
--Don't lose hope if you don't have the exact reservations you want. Checking the night before even has yielded some nice spots.