Clefts are drop-dead simple, if you have scions matching the diameter of the new branches, that'd be my plan (you can off-center the graft if the branch diameter is greater than the scion, as long as the cambium is touching). Match the cambium rings as best you can and you should have a high success rate. I'd say my success is around 60% with mailed scions (~5 days old), 80% with fresh/day-of scions on mature trees like you'll be grafting to.
Veneers are useful when I'm grafting to larger diameter branches, but they are a little trickier, in my experience. With the diameter of those branches, I would not go that route. You'll notice little green pointy shoots emerging a few weeks after you cut each branch off, it'll take at least a month to get new branches that are graftable. I'd be cutting your first branch(es) now to catch a few months of the remaining growth season. You'll still have plenty of time to plan your attack after you cut.
Having a good idea of what you want the final project to look like when you start is important, that way you can choose which new branches you'll allow to develop and remove the rest as they emerge (you want all the energy going to the desired new growth). That said, don't be too aggressive; if you want 4 new branches, I'd let 6-8 develop in places you select and graft to all of them. You *could* get all takes, but the odds are a few will fail.
I didn't see you mention how comfortable you are with grafting. If you are new to it, you need to get your grafting kit together now. There are lots of tool options, you can find recommendations on here. You'll also want to watch as many videos as you can on whichever grafting technique you choose. I would practice on new growth coming off the tree, get the feel of cutting with whatever blade you choose. Straight cuts are crucial to success. My first season attempting grafts to mature trees had a horrible success rate, 2 for 12 or so.