An alternative to tie the end together is to make a small eye splice on one of the end. You can then simply thread the other end through the eye and make a quick stopper knot.

I was looking in detail at some top boats at Carnac and I've also seen the system dead ending the sheets at the back beams with a shock cord on more than one boat. In addition to that I've also seen that on Mischa's Cirrus R there is a bit of velcro sewn on the sheets with a matching patch on the trampoline to park the two sheets at a specific spot so it's on the right place for Bastiaan to grab it when he raises the spi.

Actually I think that particular Cirrus R needs a complete review from someone. It's been tricked out to no end with in boom sheeting, up and down f*ck*r, some very long trapeze height control line, some creative placement of the spi downhaul release and I'm sure I'm forgetting quite a lot of it. Shame I didn't have a camera!