I tend to keep my hands at 9:00 and 3:00 with thumbs just over the lateral spokes (a habit from my racing days) - so I'm only on the cord with turns - and I appreciate the extra grip in that scenario...
The smaller diameter butchers string is good, Its cotton so tends to lay flat when wound under tension. The turns but up nicely and don't move and its supper soft on the hands whilst giving the grip required.