Probably the most tricky part about the lug rig is getting the battens right, and expect that it may take some experimentation. Their function on this sail is not really to pre-shape the camber under tension (as they would on something like a Hobie Cat or sailboard) but rather to simply support that big mainsail roach, which would collapse without them and hopefully, do it without screwing up the rest of the sail's shape. To a somewhat lesser extent, the full battens can also make reefing the sails easier.
As far as reefing goes, the basic style of these old fully battened canoe sails is a throw-back to the old cotton sail days. When reefing, the batten was used to evenly pull down a big slab of sail and the cotton cloth below the batten would mash down into a small bundle without putting up a fight. Modern Dacron is a different story because of its stiffness and if you want to avoid creasing the heck out of it when reefing, you have to be pretty careful as you bundle up the excess cloth at the bottom of the reef. You can't expect to be able to simply pull the batten down and have everything fold up into a tidy bundle all by itself. Since the only function at all for the batten in the MacGregor lug mizzen is old-style batten reefing, which Dacron doesn't do particularly well, you could make a pretty serious case for leaving the batten out of the mizzen's plan altogether. The sail would work just as well, or possibly even better (less weight and likely a bit more shape), and the mizzen has no roach that needs batten support.
For the big-roached main, you do need the battens and you're going to want to taper their thickness very carefully. I usually specify something in the 1.25" by 3/16"-1/4" range for batten stock. Ash will work, spruce, fir or maybe even cedar could also do the job if you're careful not to step on them. The aft (leech) end can be sanded smooth and finished pretty much full thickness. From about the batten's middle forward though, you want to gradually taper their thickness. On wooden battens, there is a limit to how much you can thin the stock before it gets too flimsy to be practical. A final thickness at their forward end of 3/32"-1/8" or so (like a paint mixing stick) is about as thin as you will probably want to go for durability reasons.
In use, the taper you put into your battens will be one of the primary determining factors in how much draft the wind can put into the sail, where in the chord its maximum depth is located and also how full or flat the sail's luff entry angle will be. These three items are all major factors which determine how well your sail will perform and battens which are too stiff are perfectly capable of defeating any draft or shape that may be cut into the cloth.
This is an instance where tapered, factory-made fiberglass battens may be far superior to wooden battens. With fiberglass, you can have extremely thin, very flexible forward ends on the battens without them becoming too fragile to be practical. It would be tempting to use glass battens and maybe cheat a bit by using epoxy to glue a layer of veneer over the last 12" or so of the flat sides at the aft end, so anything hanging out of the pockets would at least look like it was a wooden batten.
