I had been getting better at big cubes of late - not like actual better, just better for me. For 4x4x4, I'm under 2 minutes once in a while, and for 5x5x5 I'm under 5 minutes nearly half the time now. I finally felt like I could take another swing at my 7x7x7, because of those improvements. For 2x2 to 5x5 it takes me somewhere in the ballpark of 6 times whatever the WR is. (Here's a new WR on the 5x5x5 by Feliks Zemdegs.)
By that logic, I should be able to get my 7x7x7 time down to around 15-16 minutes - my best previous time is 37 minutes and change. Here's another one from Feliks, this time on the 7x7x7.
It's not even like I was sure that it was going to happen, but I just feel like I need to be in the right frame of mind to make progress and do well. The bigger the cube gets, it reduces the number of times you can practice it in a session, and I have to say that I haven't practiced 7x7x7 that often at all. Part of it is that I get nervous about pushing those little stickers around with my hands when I'm turning the cube, so maybe I'm going to have to think about finding a stickerless 7x7x7 at some point. I don't think I want one of the pink ones though, the colors aren't high contrast enough for me. I'm sure that the other part of it is that my 7x7x7 is a V-Cube and some of the newer cubes have a better mechanism than the V-Cube does.
But, this morning, I was really ready to do it, and got 1:47 in AND POPPED OUT A CENTER PIECE! Frankly, I'm a little bit amazed that I was able to get it back into place without major disassembly.
I started typing this once, and thought that it was going to be about failure, but decided that I had to do it again. I just re-scrambled from the partial solve for several minutes, took a deep breath, and started the 7x7x7 again. It was 27:12.21. Certainly it wasn't 15 minutes, and I'm sure I burned a few minutes making sure layers were correctly aligned so that I didn't pop a center piece again like last time. Hey, it's 10 minutes better than my previous, so I'll take it.