when you go neutral your wasting precious frame time. You can easily fuck up the red parry window by doing this. I think it would easier\safer just to slam it forward\down. 2-3 frames is hardly enough time to go neutral, see the frames then tap forward. Hell, theres barely enough time to slam it. I dont see why you would add an extra step.
I dont think you can slam it faster than 2-3 frames. So in theory, slamming it everytime when you need to gives you the best chance to red parry. When I say slam I mean hit fwd\dwn as fast as you can from block. I think its humanly impossible to to hit fwd\dwn from block in 1 frame. If this is true, all you would have to worry about is what move (hi\lo) their going to throw and what speed for the parry. This is how I do it and ive done it a handful of times when I really needed too.
ryus sa1, dudleys uppercut super, chungl li’ sa2 (red parry after she switches legs) these are easy when you talk about red parrying and you can keep on parrying pretty easy after the red. Red parrying does take practice. Once you learn the timing, all you have to do is apply it to what move and what speed.
I guess if neutral is working for you go ahead and keep doing it. Different people have different methods. Doing it is much more important than how you do it.