You may be spending a lot of effort for no real reward. The small amount of archaeological evidence suggests that shrouds that early may not have been served, although most of the evidence is from northern Europe, rather than the Med.
As just one example, the only served cordage found on Vasa is on the clews of the boltropes in the sails and the gun breechings and breeching tackle block strops.. The finds included a set of seven shrouds from an older ship (taken on board as breeching material), which clearly had never had serving. There are some shroud remains from Mary Rose as well, but I do not know if there is any serving.
By the 18th century, partial or full serving of shrouds was relatively common, traditionally the lower parts of the shrouds to protect from water, and all of the foremost shroud on each mast to protect it from abrasion from the course yard and sail.
Fred