I'm confused, the reason you use the 1 1/4 3 strand is strength and bounce. A splice is a weak point, and the smaller double braid you can cleat is a weak point.
Go with 12 strand, 1 inch - strength is same, fits and has bounce. It's also better looking and coils without hockles (it's what I use for a mooring, albeit 3/4 inch).
Otherwise your best bet is a modification of the single strand eye splice here (page 6) http://www.neropes.com/Resources/84906_NEROPE.pdf