QLDCruiser said..
How about Dyneema Ocean 12? This is single braid dyneema (=spectra). 4mm has a breaking strain of about 2t, more than 8mm double braid. But I'm sure the 3mm, at 1.1t, would be plenty strong enough. It is incredibly light, has low stretch, flexible and slippery, and very easy to splice.
http://www.ropegalore.com.au/4mm-dyneema-rope-sold-per-metre-free-delivery/
I'm not familiar with the application - if you need to apply significant tension by hand, this stuff would be no good on its own although you may be able splice on a tail of double braid.
Here is a video of my Fleming on its previous host, an S&S34 mid Atlantic. You can see the control lines working to move the tiller. MB has a tiller.