The way I decided to do this was before taping my quilt back to the floor, I stuck a straight pin through the centre, sharp side up. Then when laying the layers on top, I just had to make sure that I placed the centre first. It was a little challenging, because I also wanted to line up the corners and the centre seams of each side, so swivelling the fabric around on top of the batting was a bit of a pain. In the end I got everything pretty well centred.
Once all the layers were basted together, I found a small bottle cap to mark out a circle in the centre. In hindsight I probably should have just started in the centre and spiralled outward, but I thought a circle would look better. Oh well.
I used my normal presser foot for this, and think (again, hindsight!) that a darning foot would have been easier at this point, because the circle was so tight I had a lot of trouble turning the quilt. Eventually I got it, after a few false starts.
Another thing I'll say that would have made my life much easier had I thought about it. I recommend going CLOCKWISE in your spiral. I started out anti-clockwise, and realised as soon as I got a bit further out from the centre, that this meant that at some point I would be trying to swivel the entire bulk of my quilt through the harp space (that's the bit in between the needle and the arm) of the machine. Silly me.
Fortunately, as you can see, this quilt was fairly small so it all fit through the machine and was only a little annoying at times, but if you're doing a large quilt in this fashion, it probably would get really difficult. I suppose on the flip side had I done it the other way I might have struggled with the bulk of the quilt pulling off the table, but I could have fixed this by moving my machine to a better part of the dining table.
Here's the result! I had some issues with the fabric warping a bit. Possibly a walking foot would be a better choice once you're out of the tight inner circle, but I don't yet have a walking foot. So it's a bit wonky in places, but I like the overall effect. I didn't do the spirals too perfectly. Not only did I think this would make the process much slower, but I also thought that if I tried to make it perfect, I'd undoubtedly notice any imperfections much more. So while I used my presser foot width as a rough guide I made sure to just do it in a rough sort of way.
Closeup of my somewhat wonky lines.
Here's what the back looks like. There are a few places where there are some wrinkles in the backing. It REALLY annoys me, but the majority of them were so far back towards the centre that it would have been an absolute nightmare to unpick and fix, and I only noticed at the end. Oh well, live and learn. Since this is just for Button, I'm just leaving it. If I were ever to bring a quilt to any kind of contest or festival or whatever, or if it were a gift for someone else, I'd probably be much more persnickity, but hopefully Button is not going to mind.
Now my next task is figuring out what to use for binding. I have a lot of extra stripey fabric, but I'm not sure if it would be better to just use white, as it's a very busy quilt as it is. But for now, a nap!