Thanks Maxime
I have a feeling you are probably correct in the first point you make, in regard to halyard and other control line forces - if only because when it all boils down, this is the angle of the halyard force vector (when all the other forces are in play it may vary slightly from what is shown on the plan). However, the CoE offset demonstrated by Arne does help one to form an understanding of what is going on, and is particularly illuminating in regard to sheeting forces - and the heavy helm which tends to develop with most cat rigs going down wind (of which, Amiina 2 or any highly mast-balanced rig will likely be among the best behaved).
Your second point concerns me a bit, and here is why: what you wrote is perfectly correct (in the static situation). Below: same outline, different moment of force about the mast.

But you are attempting to explain the (static) balance forces, whereas explanation is not the purpose of the definition. The purpose is of the definition is purely to be unambiguous in the design of a SJR sail, so that lofting mistakes are avoided. The slot won't vary much - it is specified, perhaps a little arbitrarily, as being equal to the diameter of the mast, and I would regard it as a constant, not a variable.
Within the bounds of what is reasonable and likely, I think the definition we have been using, is appropriate and can be made to unify (sort of) with the standard definition of mast balance for contiguous sails, and allow (sort of) apples-with-apples comparisons.
A definition can be quite quite arbitrary, and it does not matter what it is, provided everyone understands and uses the same definition when bandying numbers around.
The definition I gave (and Arne used) for mast balance - the proportion of a lower batten which is ahead of the mast centre line - is in accordance with what Slieve intended when he described his SJR sail as having, say, 33% "balance". This high mast balance is thought to be close to the limit of what will work safely, and anyone fooling around with different definitions of their own will create ambiguity and might risk failure in the making of a SJR. You can call it what you like, and leave out the word "balance" altogether if you prefer, but this is the rule to use when lofting a McGalliard SJR sail: Keep the slot width about equal to mast diameter, and do not go much above 33% of the sail outline ahead of the mast centre line - unless you want to be a pioneer. There is reason to believe 35% may be possible.
Measuring along the length of a lower batten is near enough and good enough, and less likely to lead to error.
(And do not go much below 33% or there is no point in SJR , but that's just my opinion).
[If you start analysing width of slot, area of jibs etc etc someone is going to get it wrong, and over-balance, and then others come along and blame the rig for the failure (or blame the very principle of higher than normal balance, as happened before). Call it a rule of thumb, if you prefer. At this early stage in the development of the rig, perhaps one can be forgiven for being a bit "touchy" about it. Remember, this "definition" is for amateurs (like me) not for aerodynamicists.]
Arne wrote: Hasler and McLeod mention the option of having downhaul spans. These are meant to help reefing when sailing downwind (without needing to round up first).
To avoid confusion here, the spanned parrel-downhauls used on a SJR (here and here) may not be of much assistance in lowering the sail when reefing down wind. I've never had to try (I mean, never needed their assistance for that), so I don't know. I suppose they would help?

Above: two forms of a spanned parrel-downhaul pair. (McGalliard). Serendipity has a third variation, which I prefer.
I must point out, anyway, that reefing downwind is easy with spanned parrel downhauls because as soon as the halyard is released they go slack, allowing battens to fall down easily. If down-wind pressure on the panels were to make it impossible to lower the sail, then you might have to round up, because pulling on the parrel-downhauls and tightening them doesn't actually give you a direct downward pull. I just don't know, can anyone help?. If a conventional set of control lines is used together with a set of downhauls which are solely downhauls - that is maybe what Arne is talking about - then you perhaps get the best of all worlds, but what I have been trying to suggest all along is: this would mean an awful lot of control lines which, with SJR anyway, would all need to be adjusted at every reefing event.
Arne - it seems to me you have opened up a new development pathway for SJR which is worth trialling. I am very tempted to pull the top triangle off Serendipity's sail and give it a new (longer) yard and new upper section, like your HM style, just to see what happens - with a view to examining the control lines necessary, rather than performance. Next winter maybe. Thanks for your creative input Arne.
Here are four more non-McGalliard SJR variants:
The catamaran sail is a crude Amiina look-alike, with six lower panels. Its not my cup of tea, but David likes the look of it. The ketch scow (Wayward) has a split mainsail - interestingly in this photo the mains panels comprise centre panels only, the shelfs have not yet been made and the camber is achieved by differing-length temporary "Thai lashings". (Its a "shelf-foot" sail with the shelfs missing). It has five lower panels. The single upper panel is a polynesian crabclaw (negative roach). I believe Dave Z is very happy with it. The schooner (Fly) has a heavily forward raked foremast carrying a 32 sq m split sail to the owner's design, with two upper panels, five lowers, and a rather shortish yard. The sloop (Hihi) appears to be an unraked (vertical mast) version of Fly's fore sail, with one less lower panel. It would be interesting to know the sheeting and control lines used on these rigs, and what their owners have to say about their performance.

For now, I still prefer the Amina mk2 sail. And I do think the raked Poppy sail would look lovely on a SibLim 10m, if it could be made to work without too many control lines (which, I have my doubts. David - what about just setting the mast plumb?).
Here is a familiar photo of Amiina, slicing through a short chop and smoking along under her old Mk 1 sail

Thanks those who chimed in. I was hoping a lot of people would add to this thread, with descriptions of their own hands-on experiences of SJR . Please do.
Currently the discussion seems to have settled on panel size (and number), control lines- and upper sections, as introduced by Arne.
There is a lot more to be discussed in the New Year.
I hope everyone following this thread will have a safe and happy Christmas.