I can't say I've done experiments on the effect of 'scatter' winding. As a coil winder of years ago I could comment that neat, side by side winding increases the self-capacitance of the winding. This might cause strange resonances at high frequencies. Scatter, or 'Pie' winding reduces capacitance, hence you will see it in old radios for high frequency work. unfortunately it also causes wires to cross each other with the potential of shorting each other out. You can reduce this by dipping the coil in wax. This stops vibration of wires and the resulting erosion of insulation. Of course it also reduces the number of wires you can get in a given coil size so output might go down. Would love to hear how you get on.
Yes, winding coils neat and tight may increase the self-capacitance, as compared to loose scatter winding. But I haven't seen that that has any noticeable effect on the sound of my pickups. Not in our frequency ranges. The main reason why I like winding my coils neat and tight is to increase the definition and clarity. Pack all the wire tightly into the densest area of the magnetic field. That makes the coil more powerful, so it responds to the tiniest bits of string movement. That's also why I like using very large size magnets, to get the field more fully saturating the coil.
We all "pot" our pickup coils to prevent microphonic vibration. Most folks use wax, like Leo Fender did