help cleaning up my finger style?

[Sec-Def]

as some of you may have noticed I recently moved on up (down) from a six string to a six string bass.
as an exercise in both production and bass playing I decided to cover (somewhat half assedly) "favorite things" (sound of music) into a drum and bassy acid jazzy thingy.

so as I'm recording the bass line I came up with, I noticed something odd.
it's sounds as if I'm playing a two string instrument with two dozen fingers.
after paying a little more attention to what I was actually doing I noticed that every finger smack up
against the muted string above it (usually with the thumb) , this adds allot of noise and gives that un-precise
too many fingers sound. it gives an extra thump to each note.
I'm trying to get as distorted a sound as I can without it getting too noisy and harsh. so my playing has to be as clean as it can. (considering getting flatwounds even).
so any advice as to how I reduce this? I tried plucking the strings upwards, coming down diagonally from the bridge
towards the "in between the pick ups". but I'm not sure how sustainable that really is.
any one had this problem? any one has any advice as to reducing this?

[Addison]

Try playing closer to the bridge since there's more tension and it's a lot harder to get the strings to flop around back there... and maybe soften your touch a little bit.

That's usually a good place to start.

[Sec-Def]

I'll try that thanks addison!