Instead of a laser gauge, you could try using a camera hooked up with some edge detection software and use that to estimate the width. It probably wouldn't be as accurate, but it would definitely be cheaper.
You'd be looking at very subtle variations in the color of single pixels, so you might as well just use a single optical sensor and light source into a single high res adc, using intensity to measure thickness.
At some point dust in the air will be a limiting factor.
For high accuracy, the brightness is really more the limiting factor, as most of the edge finding/binarization algorithms use a intensity factor for cutoff. I used camera measurement for small pieces of tissue samples in biomechanical measurement (~1mm x 5mm). We had a small window in our lab, and cloudy days would distort measurements. I solved it mostly by going to a SLDR camera from a handheld and a backdrop with a type of luminance chart. Much more accurate than calipers for soft squishy (and wet) samples. See [1] Figure 2E (pg 22), you can average out small variations pretty readily.
Though your idea of a light source and adc could work well if you put it in a darkened enclosure. It’d probably require a bit more hardware design or tuning but the software / microcontroller side would b simpler. A RPi PiCam with a macro lens would work well too, but the reverse with less hardware tweaking and more software.
At some point dust in the air will be a limiting factor.