Mainly what the others have said, but as for specific advice:
Centres: For the first four centres, there aren't really any specific tips to give, other than to practise a lot. For the last two centres, check
this list to see if you're doing them inefficiently.
Try to plan as much of your first centre in inspection as you can; with colour neutrality, it shouldn't be too difficult to plan a 2×3 block more than half the time. (Practise with unlimited inspection time first, then when you're comfortable with that, practise with only 15 seconds of inspection.) This should also help you with seeing how to form bars/blocks with the other centres, although you won't have the luxury of 15 free seconds of inspection with those.
Edge pairing: Use freeslice or AvG, if you aren't already. For freeslice, when you're done with forming a tredge, don't think too hard about which tredge to form next. Just pick whatever edge piece you see first, insert the pieces needed to complete it, slice, and move on.
For the last two edges,
learn some algs. You should learn all the non-parity cases, as well as the "O-parity" and "2-swap" cases. The other parity cases are worth learning eventually, but have less of an immediate benefit.
333: Try to grip the cube on the X-centres (the "inner corners") to prevent the inner slices from moving around during your 333 stage.