Is it the 4-3-0-0 sequence you are having problem with, or is it the drilling 16-16-16-16-16 stuff?
When you do 16-16 (hajiki symbol on this second one), you want it both notes to sound the same even though you will just be striking the string with the bachi on the first strike.
Consider that what you should not focus on first positioning your finger on the string and then move it out. If you do that you might get stuck into feeling that it is a 2 part action. It should really be a “flick” where your finger is set in motion in a steady pace, and on the way it gets in contact with the string and then slips off the string, all in one linear motion.
When it comes to a 4-3-0-0 sequence or similar it is a bit different. In shamisen music you will find a lot of these sequences, or similar ones. Basically when you strike the 4 with the bachi, you have already positioned your index finger on 3 and ring finger on 4. This time, you thereby start with your finger already on the string you are about to “flick” off from. It should still be a linear steady, it’s just the starting position that is changed. If performed properly, you should hear the 3 note as your index finger is there.
As Kevin says you might be angling your hand in a bad way. Think about where you can “flick” your finger with as much accuracy, power and speed as you can. For me I angle the hand so that it’s 30-45 degrees to the neck depending on where on it I’m playing.
I am no master of hajiki, but this is what I’ve experienced!