First off, you have a lot of work ahead of you no matter how you train. Most people break a minute without paying any mind to how good they are at reading the previews. As a disclaimer, I don't believe what I'm about to say will be very helpful in the short run. However, I do believe it was extremely helpful, for me at least, in the long run. It helped me develop good habits.
You asked about what I call "blind active piece training." This is what it looks like:
So, playing like this forces you to know exactly how to place every piece in every situation, strictly on "instinct." It's fantastic for solidifying your finesse knowledge. I suggest training on this until you come within 120% of your best regular sprint time. If you'd like to try it, I've explained how to tweak your settings in this post
Now, you asked specifically about becoming better with previews. Well, we can take this concept one step further: blind training hard mode. You simply cover the next preview piece with electrical tape or something, and then now you must always try to remember what next piece is coming. You have to keep the active AND the next piece in mind at all times. It was extremely difficult for me at first.
I stopped training with this method after I could consistently play with the next three previews covered. Although, I still sometimes practice regular blind mode. I hope this helps.