Not sure I understand, did you try to ride it without the 3 degree stabilizer adjustment and there was a difference, or is it not the topic ?
I assume you mean minus 3 degree adjustment so it pulls a bit more down thus initially feels stable, right ?
Assume it is beyond the topic though...
There are several parameters that determines yaw stability, fuselage outline, mast position, wing design, washout or not etc.
But if these are pretty given, then yes, the rudder is the determining factor.
A stabilizer which is swept up or down, or has winglets = rudder, exactly the same thing.
It is not that easy though - as many of us like a really "loose" foil for tricks and waves, and this requires at least a smaller stabilizer.
Stabilizer size and rudder is a bit different though, as some like a foil that can be turned yaw wise thus little or no rudder effect, others like to have a tracking effect of the rudder so it does not feel as nervous (like you describe, nose wiggly).
Exactly the same thing as with waveboards and fins - two different opposite likings with each their advantages.
Regarding stabilizer SIZE, somewhat the same applies, as a smaller stabilizer means a livelier foil in both yaw and pitch, so more twitchy and difficult to ride, but more fun.
Till some extent, as when too small, it becomes "no good".
I've got a supersmall stabilizer without winglets nor V, and it is really fun often, but can also be too twitchy and I opt for a still quite small but a bit more upswept shape, so still lively but still feels good in terms of desireable tracking
For learning things, a big stabilizer and rudder effect, is much easier.
I took a look at the LP stabilizer(s), and it is almost flat with only really small winglets, so not much rudder effect no, which explains your experience, some dont like it others love this.
Short story is, rudder effect means a lot, but you gotta try to find your personal liking for your specific style, to know what you like
It was not an answer to your question, I know, but the yaw stability is the outcome of many design parameters and not that easy to determine without looking a the complete foil design, and not just one or two factors.