And finally, the glue has set and I've applied 1.5 grips.
The handle still feels a thick, but I can now get my hands properly round it. I tried it with just one grip and it still didn't feel quite right. I applied the extra half grip to the bottom of the handle and something amazing happened. The bottom now feels noticeably thicker than the bottom, which is what I find comfortable, and the pickup seemed to improve.
Interestingly the dead weight before I took everything off was 2lb10 & 1/8. With the same grip set up it's now 2lb10 & 3/8, so reducing the girth of the handle has increased the dead weight!
Now all that's left is to knock it in and apply a scuff sheet.