Which range/distance sensor to use?

Hi. I'm trying to find good distance sensor for my arduino. I know about ultrasonic sensors like HC-SR04, but there is one big problem. Measured area must be too big, with longer distances. Around 800mm I think. My project is measuring hight of paper stacks, standing side by side. From above, of course. If I have 3 stacks one next to another like |_| (high,min,high) I can't measure the middle one, because this stack is only 300x300mm (and no, I can't just push stacks further) and ultrasonic sensor hits the sides of left and righ stack - and it equals bad measurement.
So what I need is:
-measuring distance: to 2m
-accurancy: under 1cm
-measured area: Φ 30cm

I know, there must be something, fe. IR or laser sensors, but it really makes me problem to find sensor, with these requirements and with good datasheet. I really cant effort to buy 5, or 6 different sensors just for making experiments.

Thank you for any suggestions. I will appreciate it so much.

Scanning lidar #227 The ugly truth about LIDARs for obstacle avoidance (RPLIDAR A1, Arduino, ESP8266) - YouTube

mikb55:
Scanning lidar https://youtu.be/AERfie9wlWM?t=140

Thank you for suggestion, but this radar is slightly overexposed, isn't it? I'm looking for simple one way sensor to measure only one "stable" stack. For second stack, another sensor will be there....and so on.
Please, I am sure someone knows it. If someone have any other ideas how to solve this problem, please write. This problem is similar to IOT, i think, so it must have solution.