* Points on a spline and instances on a particle spline are not interrelated. The particle spline populates the spline with n (= number of particles as defined) with equally spaced instances.
* If you require an irregular spacing: For precise control of the PM, you will have to use a flat path (= line on a 2D / 3D curve) and deploy a particle mesh with a polygon base.
* Shifting points on a spline does not show in the editor (the particle spline remains static) but it does show in an animation (record points or whatever).
* To update ad hoc / in real time: Just toggle the visibility in the object browser off / on.
* Given your existing spline:
1 add an extrusion modifier to create a narrow strip
2 generate a particle mesh; point type, repeat order, alignment off
3 populate with object required
4 add an second dummy object (in my example a bone); this can be a real object with visibility toggled off
* You can now move the points of the original spline and the objects will move in parallel along X, Y and Z
* Maybe a personal matter, but I find free-floating points frustrating to handle. As they are not linked to some visible geometry, it is difficult / impossible to conceptualise their position in 3D space.
* I much prefer to use constructors, visible in E-space (maybe wireframed) and hidden in R-space. YMMV