Honestly, right now it's just tied to it with bowlines. I know this reduces the strength of the line by aprox 40%, but it was kind of a temporary fix at the time. I noticed some serious fraying on the lower backstay in the crimping and needed it replaced that day so I could still participate in a race. You may have to get a little creative with attaching it.
I'm probably going to replace my rigging and lifelines over the winter and may have a better answer for you then. I'm definitely using dyneema for the lifelines. I may replace the whole backstay assembly with dyneema and leave the shrouds and forestay as cable to have the use of turnbuckles. I just thought I'd throw it out there as a quick and inexpensive fix to get you back on the water. It worked for me.
I know a lot of people that are replacing all of their standing rigging with dyneema. A friend of mine just replaced all of his on his Corsair 24 with dyneema. It's lighter, stronger than equivalent size cable, doesn't stretch much, self-lubricates, doesn't degrade in UV, has great abrasion resistance, and floats. Also, if it does fail it doesn't fling ripped metal back at you.
Here is a cool video comparing dyneema and cable: