Probably not. Since you've mentioned the sound difference is not much, I don't think you should. An upgrade should make tremendous difference.

As for the action (the gap between the string and fingerboard), that can easily be fixed by sending your violin to a luthier. Look for Mr Tia from Amadeus Violin House. I always send mine to him. My viola used to be so hard to play, after he filed down the bridge, it plays like butter now.

As for the bow, different violin will react differently to the same bow. I think it's a mix and match thing, you might have a very expensive bow, but it might not be as nice as a cheaper bow. That's why it's very important to try it together first.

So I don't think you should upgrade from 3k to 6.6k violin. The most important thing is the sound, and since that's not much of an upgrade, you'd do better to stick with your current one. Just send it for setup.

Also, if you want to improve your sound, maybe you could try out different strings. The difference in strings are phenomenal, not like guitars where string brand doesn't really matter much.

Warmer:

Pirastro Obligato
Thomastik Infeld Red (kinda same sound with Obligato but cheaper)
Pirastro Eudoxa (Gut strings, standard before Dominants)
Pirastro Olivs (the king, but RM550 per set).
Corelli Crystal (Only use this if your violin is very bright, as I've heard it's really dull)

Louder and more vibrant:
Pirastro Evah Pirazzi (heard reviews it doesn't last long though, expensive price)
D'Addario Helicore (steel strings but sounds like a brighter synthetic strings)
Pirastro Gold (Gut strings, but somewhat bright).
D'Addario Zyex (Damn loud)


Balanced tone:

Thomastik Dominant (The standard, but change that E string to something like Pirastro Gold E or Goldbrokat)
Pirastro Tonica (A bit cheaper than Dominant)