You guys are on the right track. Instability at a distance is due to the velocity decaying much faster than the spin rate.
A pellet gets a lot of its stability by way of its shuttlecock geometry. For example, if you take a badminton birdie and toss it sideways or backwards, it will immediately right itself and lead with the nose. Granted, a pellet isn’t quite so forgiving but it has a similar behavior.
Thus a pellet does not need much spin to keep it flying straight. The purpose of spin is to even out slight variations in the pellet’s weight bias (a little heavier on one side than the other) or slight geometric/aerodynamic asymmetry (a little ding in the skirt, some subtle mold flashing, etc.) Without the spin, these defects would cause each pellet to veer off in some apparent random direction. But by spinning it, the defect is constantly changing the direction it wants to veer off...just imagine it as an invisible hand that nudges the pellet at the 3 o'clock position, then at the 6 o'clock position, then at the 9 o'clock position, then at the 12 o'clock position. And around and around it goes, constantly being nudged back into some averaged middle trajectory.
However if it’s spinning super fast, that imbalance causes it to wobble. Intuitively, I think of the drag as something of a parachute trailing behind the pellet. When the pellet is moving fast, there’s a lot of drag force tugging on the skirt that keeps the nose pointed in the forward direction. Then as it slows down, the parachute is no longer pulling as hard so it’s easier for the uneven force of the spin to cause it to wobble.
How badly it wants to wobble goes back to how imperfect the pellet is. If it is supremely balanced, it may not wobble at a great distance. If it is poorly balanced, it may start wobbling or spiraling as early as 40 or 50 yards.
