Daniel,
For a long distance serious cruising boat, my view is that the luff and leech should have some weight and stiffness to them, to slow down any flutter that might happen. A fluttering leech is the way to destroy a junk sail, over time. My preferred way is to add a very wide tabling. Webbing is absolutely unecessary, except in cases where the sheet is tending to chafe the leech, when a short piece might be added on top of the tabling. I would suggest that you cut a length of Odyssey into five equal widths of about a foot wide, and then fold them lengthways to leave four inches on one side, eight inches on the other. Then use double sided tape to secure this strip to the luff and leech, and sew close to the edge of the sail, and close to each of the inner edges. Make wide overlaps of sections of this strip at each batten position, and you are well on the way towards providing the necessary patching at these points.
The other thing that will cause a fluttering leech is to cut the sail with straight edges to the panels. The pull of the halyard tends to bend the yard, and I always add at least 1% rounding to the head of the sail. Up to 2% can be used without problems. Wherever there is a seam between panels, I add 0.5% rounding, with the maximum depth towards the luff. This makes all the difference, though it might only be 3/4" . It doesn't show up as meaningful camber, but it keeps the leech taut. For this reason, I suggest that you set the topmost sheeted batten at a slightly steeper angle than the lower ones, and cut the three top panels separately, with minimal rounding, and then cut the lower four panels together, with minimal rounding top and bottom.
Two lines of zigzag stitching per seam is fine. There's never any need for triple stitching, the loads are low in the body of the cloth. The enemy of the seam stitching is chafe from the topping lifts, and three lines of stitching chafe just as easily as two.
If you are going for grommets and lacing (not my preference, pockets are easier to do and take less time and money), you need to cut some strips about four inches wide and sew them on along the line of the batten. I would recommend at least three thicknesses in total, to hold grommets without them pulling through. The threads of the cloth must be in line with the pull, or you will get some very weird creasing. Don't reckon on tensioning the sail out along the battens very much, or you will induce creases. Just make the battens 1% longer than the position on the sail, fix them flush at the leech, and apply only minimum pull as you lash the forward end. One of the hardest jobs is to roll up a full sail, to pass it under the machine as you sew these strips on. That's why it makes sense to make separate panels, even if they have vertical seams, and sew them together with a four inch overlap, and adding a four inch batten strip as you go (thus getting three thicknesses, with the batten strip protecting the panel seams from the batten - important). If you make the lower four panels all in one, I'd add the batten strips to the three batten positions on this piece, before joining on the upper panels, one at a time, and adding their batten strips, one at a time.