Made my model rig 1:20 scale. Without the sail cloth, since cambered sails don't control the batten position much, I wanted to see if the yard/battens/boom with bolt rope can set the right shape without HK parrels. The idea being to do away with HK parrels, which press into the sail, spoiling the shape at the luff.
Pictures of my model are
here.
First I tried with just 3 lines holding the whole rig up: Halyard, Yard HP and Throat HP. Luff wouldn't set completely straight.
Added a tack parrel, improvement but no dice.
Shortened the yard, made no difference.
(Tried adding a HK parrel (sticky tape) to one panel, fixed one batten but all battens need them.)
I also tried threading the throat parrel through a few more battens, becoming a running luff parrel, but it pulled battens into different positions, or maybe that is a problem with my rough model.
Then I added a boom downhaul, pulled tight and everything lined up! Amazing.
Conclusion so far
I don't know how much downhaul tension is required on a full size rig, probably too much!
But the sail cloth in the top 2 panels could play a part in lining up the top 2 battens if they are flat in the thin forward end of the panels. If this is the case, 3 running lines on the yard, combined with tack parrel and downhaul makes for a well set rig without HK parrels.
The standing luff parrels omitted from my model are still needed, they keep the rig together while raising sail, because before the throat hauling parrel can be tensioned, the rig goes out of control without them.