I've had trouble with the three fingered (3-2-1-2-3) technique, and after several months of trying with it I still cant get my speed as high as I would like.

The other day I was trying to work out some other ways of getting fast finger speed, and I realised I can play 16ths at around 165bpm by using only my index finger, hitting the string both down and up.

Just wanted to know if there are any ways of further improving my speed, as there are many songs I want to learn which need a faster playing hand.

Try to focus on just one aspect of it. For instance, try just playing with your right hand. Just focus on how fast you can get your tremolo picking down. Then try to do them all down the strings. Then up. And when you get that down, try doing the (3-2-1-1-2-3) motion SLOW. Just to get your fingers accustomed. As you do that, you will gradually get faster. Im telling you, take on thing at a time. This is what i did when i was learning BFMV stuff. Anyway, hope this helps.
TFor this method youll need to turn the treble right down but you can get up to ridiculouspeeds, when you use your fingers hit the string with the back of your finger as well. Most people wouldn't like the sound it makes though.
hit the string with the back of your finger as well

by this do you mean with the nail side?
because thats what i mean with the down and up with the index finger, down as normal and then almost like a flick on the way up.

Dethklok's touring bassist uses a similar style to you, he puts his index and middle finger together and does an up down motion like a pick and can go pretty fast. There's a video somewhere on youtube where he explains it.

The tone isn't all that great but since your using your index, you might as well use your middle so you can go insanely fast like spaz said.