I use the original X100 a lot (well by my standards) and I have the the minimum shutter speed set to 1/100th before the ISO is adjusted automatically. I did this because I found that shots at 1/60th were sometimes suffering camera shake which I put down to old age. It seems to be the case that as I get older I can't hold the camera so well. This was equally true of the Pentax but that had in body image stabilisation which was superb and compensated.
I
can shoot at 1/30th and get sharp results but I have to make the effort and take one or two extra insurance shots.
So, I'm not sure where that gets us
Personally I don't blame the camera design, the same is true of my X-Pro1, I put it down to getting older. I also seem to have a slight problem with moving the camera as I shoot as what ought to be level isn't always.
Try changing the way you cradle the camera and how you press the shutter release - which I'm sure you have already. I was advised to have someone watch as I shot and tell me if I was jerking it at all.
As for a half case - I find the camera just fell into my hand naturally when I picked it up. Oddly the X100F less so but I still plan an upgrade.
Mike