I'm an airline pilot so deal with stab trim every day at work. I hope the following is useful and explains what is going on:
On an aircraft the centre of mass is determined by the passenger and cargo distribution, and calculated before every flight. The stab angle is then set for takeoff based on that calculation. In flight the stab angle is adjusted for the speed we are travelling at for level flight. Just like when foiling, the faster you go the more the aircraft wants to pitch up, so we adjust the stab angle of attack to make the overall rotation zero.
When foiling, the stab is fixed, which is why we need to move the centre of mass around as we speed up and slow down. However, it might already be so far out of trim that neutral flight requires weight to be way forward or way back, which is uncomfortable and harder to make adjustments. There are two solutions to this - either move the foil in the track, or adjust the stabiliser angle (or trim as we would call it).
Stability is a different concept. Commercial aircraft (and the foils we use) are positively stable, thanks to the stabiliser. If you are flying along with the setup neutral and hit some turbulence, either in the water or the air, then the angle of attack changes on both the main wing and stailiser. Because they are aligned in different directions, the resulting change in lift on both makes the aircraft/foil pitch to counteract any upset. So if you suddenly get knocked 2 degrees nose up, the lift on the main wind increases, but on the stab it decreases, meaning a nose down rotation back to where you started.
To answer the question about stab angle and stability, the answer is yes, but we're not only talking about upsets, but also the pitch effect of shifting our weight. If you have a foil that has massive pitch changes for tiny body movements it also feels unstable.
The reason is as follows...
If you have a bigger distance between the centre of mass and the centre of lift, you need a bigger downforce from the stab. Or, looking at it the other way around, if you set the stab for more downforce, you need to have your weight further away from the center of lift when you stand on your foilboard. This greater distance means more stablity.
In the top image the centre of lift is closer to the center of mass, so little downforce is required. In the bottom one the distance is further so more is required. These forces are exactly the same as when foiling, except in foiling we are shifting our weight to keep the board level.
The top image is less stable in pitch than the bottom. If in the top picture imagine shifting the weight back 1 metre, when the distance from CofM to CofL is 2 metres. This halves the pitch down rotational force (Force*Distance)
However if you shift your weight in the bottom picture by 1 metre, where the distance from CofM to CofL is 4 metres, then the rotational pitch down force only changes by 25%.
So bodyweight shifts have less effect when there is a greater distance between the centre of mass and the centre of lift, meaning bigger bodyweight shifts are required to control pitch. But it's not the stab that is providing more stability, it's the distance between CofL and CofM.