I wouldn't start with SLs for any breeding project, to be honest. When you start a project, you want to start with clean genetics, which cannot be found in hybrid offspring. SLs will throw all sorts of random genetics curveballs into the equation several generations down the line.
Also, large breeds tend to lay late because of their size itself. The chicken's body only can produce so much energy to dedicate to things. Either growing large, or laying early. High levels of laying robs a lot of resources from the chicken, and leans them down considerably because they just can't keep up with the demand of losing an eighth of their weight in resources a day (an egg is large compared to the bird, and a massive loss of minerals, energy, etc). Most dual purpose breeds will just lay 'ok', and therefore have enough body resources to dedicate to size too.
I would suggest to make a large dual purpose breed, you may want to start with Cornish (true cornish, no cross), and some sort of purebred layer, then work from there.