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Also, you might be overthinking the jib car leads. They certainly deserve consideration, and the understanding that - generally - the lighter the wind, the further forward they usually sit. (conversely, as the wind picks up, moving them back will help tighten the foot, flatten the sail, and push the belly of the sail forward)
But the thing is, all other things being equal, you should be able to sheet that jib just about anywhere. Sure, it won't work very well, and could be downright unsafe in some situations, but it won't really cause what you are experiencing. It's a contributing factor, certainly, but there's more going on.
Check the centerboard, and also, lets do this:
What are the dimensions of your rudder? How deep does it go in the water (aka 'draft'), what's the chord (fore-aft measurment) at the waterline, what's the chord at the bottom, and what's the width of the blade? Also, when fully deployed, is it in line with the transom, or does it intersect the transom at an angle? if so, what is that angle, roughly? Is the angle forward or aft of the transom plane?
Might just be that your rudder is tiny. If so, I promise not to point and/or snicker.
... or I'm wrong.
Living aboard, currently in the Chesapeake
O'Day 37, still new to us