I don’t quite understand, Arne.
Two questions: the first is a small point, relating to your nomenclature.
The two diagrams appear to show identical junk sails in identical positions.
The CE appears to be identical, as far as I can tell, with the Bermudan CE.
And it runs vertically through the point you have marked “CE1”.
The halyard angle is shown as 5 degrees.
I can not see any diagram showing the sail in the "forward position" (which you refer to as “CE2” ) but I would expect it to have a different halyard angle from the above, yet you have said that "The CE2 position is with the junk-sail pushed forward until the halyard angle is only 5° from vertical..."
Is there some mis-labelling here, or a diagram missing? Or am I missing something?
The second question is much more important and refers to the drawing you are working from.
I do not understand your terminology "CLR1" and "CLR2"
Surely this hull has a fixed underwater profile and therefore must have only one centre of lateral plane. I note that your lead calculations are based on a point you have marked CLR2.
I don’t have a way to quickly check, but eye-balling it, it seems that the point you have marked CLR1 might be the actual centre of lateral plane for that hull profile shown in your drawing. (Or, perhaps these are just "rudder in" and "rudder out" calculations?)
Then Arne wrote: "I trust Bingham as a designer; He would not sell a number of plans without getting the helm’s balance right first..."
If that comment, and your two CLR positions, indicate that actually you have been having some doubts – then I share them. (I don't doubt Bruce Bingham, but I wonder about the public domain drawings). I must say the bermudan sail plan does look a little too far forward on that hull profile (although it often seems that way with that sort of keel so I don’t really trust my uneducated guesses).
Anyway, there is still some ambiguity here. According to the "History of the Flicka" article, after the boat was first featured in Rudder magazine in 1972 as a ferrocement design the sail plan was changed (also the displacement was drastically changed - and therefore perhaps also the underwater profile?)
These two sail plans look to have quite different CEs. The first, with its overhanging boom and fractional rig with relatively small foretriangle - the second with its shorter boom and overlapping masthead rig.

The internal layout has changed quite markedly too (for such a small boat) which possibly suggests a change in hull shape as well?)

SailboatData website shows a third sail plan - possibly a cutter rig, anyway with large foretriangle and inner forestay.

I have not personally seen a single drawing showing the later bermudan rig placed in the same drawing on an actual hull profile, in the manner of that first drawing. (Where did you get yours from?)
If the displacement was changed from 10,000 to 5,500 lb !!! (according to that article) then maybe the under water hull profile changed too?
It almost leads me to wonder if there are two different Flicka designs. I wonder if the public domain illustrations have led us to a hybrid - the later sailplan and later internal layout superimposed on an earlier hull profile drawing.
I hope I am not adding useless confusion, but a question mark still remains in my mind. I do not trust my limited ability enough to say there is something wrong - surely what I am suggesting is highly unlikely. Perhaps there is an explanation which I am missing.
I would quite like to see an actual set of plans as sold by Bringham, I am not sure if public domain illustrations can always be relied on.
At the end of the day, I suppose Kristoff's Flicka is the later version, and that the bermudan CE position which you have adopted as a basis for your junk mast position is the correct one.
I guess that's all that really matters.