Hello Rodney,
Let's see what we can do to aid you in your decision making.
It has been quite commonly found that a flat sailed junk rig is slow in stays. This is simply because there is so little drive when pointing high that the boat cannot be "powered" through the tack. This applies to Hasler sails, mostly. Where the sail is flat, but the planform is fanned, there is actually a useful amount of camber developed when the sail is allowed to twist a little. This is the "fiendishly cunning chinese" way of adding camber that Blondie Hasler did not take fully into account, choosing instead the more easily designed geometry of the parallelogram panels combined with a couple of triangular top panels.
As to the modern sail types:
1. The split junk is showing promise as a racing and coastal cruising rig. It is fast, there's no doubt of it - if it is made with exactly the right geometry of jib/slot/mainsail. I'm not sure that Slieve, the originator of the variant, thinks he has the final answer to the shaping of the jibs. From the open sea sailing perspective, I would not like to use it until something has been found to prevent the jibs from flogging when empty of wind, a very un-junk-like characteristic. The jibs hang down and obscure the view forward when reefed or furled. The type is not appropriate for a two masted rig, in any case, so I think you can discount it as an option for re-rigging a Freedom.
2. Hinged battens have been used successfully by some and unsuccessfully by others. They depend on having very soundly engineered hinges - which are not available commercially, and so you would have to have an engineering background to take on the job of designing and making your own. The hinge has to be further aft than is desirable for getting the camber in the right place for maximum drive. Otherwise, it tends to hinge the wrong way, or to fail to articulate at all (a question of how much balance area there is forward of the mast compared to the position of the hinge aft of the mast). Hinges have the advantage of being used with a flat sail - which is easier and quicker to make.
3. Yesterday, I sailed on Annie Hill's Fantail for the first time, with the sail I designed for her to make. It is fanned, and has 6% camber in the lower panels. It is now set up with the standard junk rig lines of halyard, yard parrel, luff parrel and 5 -part sheet. Annie tells me that I had a smile on my face whilst I was sailing. Fantail was fast and lively to windward, yet she retained the docility and ease of handling of the flat sail. Due, I think, to the convex curve I added to the luff, we were able to dispense with the Hong Kong parrels that are usually needed with a cambered panel sail, resulting in a much better setting sail on port tack. I'm convinced that this type of sail - cambered panels, fanned planform, convex luff, straight-ish leech and stiff battens - is the best "modern" choice for a single masted boat.
However, and unfortunately, I cannot see a way to get all of these features, so good on a single sailed boat, into the rig on a two-masted boat. A fanned sail necessarily has to have a strong aft stagger to the battens as they are reefed and furled, and it is difficult to find room for the sails and the sheeting system, particularly on a short-ended boat such as the Freedoms. For my best shot so far at schooner/ketch design, look at the photos of the suit of tan-coloured sails I made for Badger before I left England. They have a moderate amount of camber in the lower, parallelogram panels, which are as deep vertically as is consistent with sheeting and handling considerations; the yards are set at as steep an angle as practicable, with two unsheeted battens in the fanned head of the sails, so as to keep each panel small for "storm sail" use.