Not sure what you mean by 'droning' ?
If you are talking about over tones, then you have to accept when learning over tones are going to happen. As you progress you reduce the overtones by the fact that both hands and your brain are syncing better.
On the fretting hand the string has to be pushed to the fretboard. Push it to hard and to soon you get an over tone created by the string hitting the fret. Push to late or to soft you get incorrect note, such as a buzzed/muted note that is not clear, so it has over tone values.
The fact that the note mat be fretted correctly first before it is plucked, means the fretting hand is always leading the plucking hand...you cannot correctly play a note that is note correctly fretted.
On the plucking hand we have the situation of learning to pluck the note clean, again when movement is being used, if you pluck to late the string is being released, so that is similar to the fretting hand not using the correct pressure to fret the note, the symptom sounds the same but the action is the opposite.
Releasing a note and plucking it late is the same as plucking a note not fully fretted.
As is plucking a note before the fretting finger of the previous note has been properly played, you may think you are not fretting fast enough by getting the fingers down, but it could be you are not releasing the previous note fast enough?
So this is not about putting the fingers on the fretboard, but actually lifting them off. But lifting them off just enough to allow the note to be true and not have the freting hand trip over the plucking hand.
In all the more you play, the more these parameters reduce, the time taken between fretting the note and actually plucking it reduces, as does the time in releasing it, fretting a new note and plucking it.
Only in the movement of music will this skill develop, playing songs that have lots of movement, learning to fret and release correctly while plucking at the correct moment. That is lots of movement, not lots of notes.
There is a phrase used that 'movement becomes movement', all this means is that if there is a certain amount of free motion being used, then it is easier to make a determined motion from it.
Look at any sportsman, they have free movement before they undertake the task in hand, they never start from a static position, there is always some form of free movement involved.
From a tennis player swaying before receiving a service, a pitcher before a throw, a golfer before a swing etc.
If you want to throw water cleanly from a bucket you do it by giving it a few sways backwards and forwards to build free motion, then release it...the water comes cleanly out the bucket in a line of motion with direction. Where as if you just throw it out from a static position it splashes everywhere in all directions.
So see your playing skills when fingering as matching up the motion of freting and plucking with the idea to reduce, not eliminate, but reduce the over tones you create, and it will develop in to a clearer sound that sounds like over tones are not present.
There are some great exercises for feeling free movement when playing.
One such example is to fret a note when plucking, then push it a little harder, then release it, then a little harder then release etc.
So in effect you fret the note so it is a true note, add a little more pressure, the note is still a true note as the adding of the pressure will not change that, then release it back to the original pressure.
Just because the pressure is changing in this manner will mean the note will not, you still have the original pressure being used, but by adding a little more you are 'bouncing' your finger muscles in a free movement.
Remember the notes does note change timbre it remains a constant, if you release it a little to much you will get that buzz/muted note, of you release it fully but keep your finger on it you get a pure mute/damp of the fretted note.
Now where this comes in to effect when playing is if you have to play a passage that is on C for bar after bar, so you are playing eight notes constantly. If you then have to follow that up with a run you start your run from a static position, but if you have been bouncing the fingers on the note as described you have in fact been using motion so your finger react better to beginning the run.
Over time you just naturally develop the bouncing to be part of your technique, as with all things, without thought as it just become part of playing, you just add a bit of free movement before any 'real movement'.
It also stops player developing over tight grips of the neck, as the constant release of the pressure will release not only the bit extra pressure use have applied, but any excess pressure you have advertently built up by being on a single note playing eighth notes for bar after bar. It takes a bit of practice but once learned it is a great tool to have in your armoury.