Gentlemen, you are asking a lot of very interesting and important questions. To understand the answers it may be worth thinking about the background of the Split Junk rig.
In my efforts to find a solution to what I saw as the weakness of the junk rig (lack of acceptable windward performance) I pictured a high balance, well cambered rig, and having high hopes in my ability to get something out of it I then started to build it. I was faced with every question you have asked so I read widely on the subject and threw in my lifetime's experience of practical rather than theoretical aerodynamics and put answers to the question to produce the Poppy rig.
I was pleased to find that it came up to expectation, and now some ten years later and with more experience I am still looking for the best answers to these questions. Who says my answers were or are the best ones to give the best possible performance? These are the problems faced by everyone who sets out to devise something that hasn't been done before. Who had ever heard of a split junk rig? Not me.
Trying to take the question one by one, -
Balance. I wanted as much of the sail clear of the mast in undisturbed air so I wanted the maximum balance that would be stable, but had no guide as to what that would be. I knew that a NACA 00 series foil balanced at just under 25%, but I guessed that I could go beyond that with a soft sail. It was only after I had sailed Poppy that I met Roger Stollery who was a leading light in the model sailing scene and who had discovered that 33% of the rig area could be in front of the mast and still be stable. Roger's balanced model rig ended up being copied to make the Aero Rig, which performed well, but had some practical handling problems.
Yard angle. The high balance encouraged low yard angle, but as this also was in line with my thinking on the sail shape at the head to reduce tip losses I was happy to go along with it.
Luff shape. Every time I look at a junk rig with a cured leech shape and a straight luff I cringe as I realise that the rig must have some high stress areas as the forward thrust of the battens at the leech must be balanced by the aft thrust of the luff. Rather than calculate the forces and sail shape I simply made a couple of string outline models which was a great learning exercise for me, and gave me easy answers. I now reckon I could calculate them easily, but that goes with experience.
Main panel camber. That was an easy one, as I reckoned that the main panels were there to deflect the air over the jibs, and at one stage I even thought of using flat panels, but in the end it seemed an interesting exercise to build a round and broadseam set of panels as a self education tool. I'm glad I did. I can't remember what camber I've used in each rig, but must have the numbers somewhere, and they've probably been published somewhere.
The split width. This is a tricky one as it seems to depend on a number of things. I've never been fully convinced by the many theories I've read about 'Slot Effect', and anyway as there would be no overlap I doubt if there would be much effect. I was more worried about letting the air through the 'gap' and not blocking it. With a Bermudan rig the mast is on the rig centre line but with the straight junk battens the mast is off set to one side and therefore blocking the air on one tack. To help I put the jib on the mast side of the battens but even so the diameter of the mast seemed to dictate the split width. The answer to me is it is a guess and a compromise. Mast drag is enormous so the thinner the mast the better as far as I'm concerned. On my smaller model yacht the jib just about touches the mast face so the split is virtually zero, but then the mast is a 3mm carbon tube. Poppy's mast was 6”/15cm at the lower section, so after trying a paper panel I tried to set the gap to allow the air to flow past the mast.
Jiblet patterns. Knowing what I thought I wanted to make, I sat and looked at a large roll of 200g/sq.m Terylene sailcloth and realised that I wanted to make a complicated three dimensional shape out of two dimensional sections and had nowhere to go for guidance. It made me focus my thoughts. To break the problem down I named the various parameters something in line with Bermudan thinking and was able to produce shapes which concentrated the broadseams at the luff corners (effectively the 'tack seam' in conventional sailmaking terms). This was further developed into the angled shelf foot idea, and suddenly everything fell into a practical way to go. But now I had invented new terms such as 'sheeting angle' and 'camber' which didn't really have a normal meaning. I suppose sheeting angle could be compared to the angle between the tack to jib fairlead line and boat centre line, though I doubt if they really are the same. In the vertical plane the actual leech will be similar to the arc of a circle as the tension along the leech will not produce any corners, so it is difficult to define a luff to leech line angle with the batten line. This is why we have been experimenting with little sheetlets (more complication which may not be really necessary??). Camber is easier as without it the jibs would be slices of a cone and produce little drive. The big question was how to balance these figures. So far I've drawn combinations of shapes and used the mark one eyeball to make the selection. I have found that camber and sheeting angle seem to work in harmony to give a pleasing shape, which does not have any inward curve of the leech (as flaps cause drag).The camber and angle numbers have increase since Poppy's rig with Amiina's new rig being the highest yet. The problem it to see how far we should go. I have material to make at least another set of jibs to experiment with, so who knows what will happen? There is no reason to believe I have the right answers to these problems, though I've been happy with the results achieve so far. There is plenty of room for further development.
Additional slots. I wanted a good cambered shape over the first third of the chord as all my experience suggests that is where the real work is done. Any further complication would be just complication in my eyes. Multi slotted rigs have been built and produced high lift, but also high drag and overall a low L/D ratio. KISS.
Mast drag. This is a major drag (not a pun, but a fact), but the only way to reduce it is to streamline it but the streamlining would have to rotate with the wind direction. The only way I know to achieve this is to bury it within a thick wing sail, and I think it is better to accept the problem and build the simplest rig which is easily built and repaired yet give good performance. Is the extra efficiency worth the extra work and worry? I doubt it for a cruising boat. KISS.
Entry and exit angles. My mention of these was to encourage readers to look critically at camber shapes. I have seen what I believe to be most inefficient cambers drawn by so called professional sailmakers and I think it would be good if sailors learned to question these experts (?). My experience in the junk rig world is that all the advances in rig development have been made by amateurs at their own expense, with the professionals trying to copy and profit from their efforts.
I hope you realise that I do not believe I have all the answers. I have faced all the questions without anyone to help, so my answers are not necessarily right. The last thing I want to do is lead anyone down the wrong path. I do intend to tidy up my notes, and hope to start early in the new year, but we'll see.
No doubt the comments above will raise more questions, but that is the name of the game.
Meanwhile I hope the New Year brings all the good things we wish for.
Cheers, Slieve