You could use a slip ring to bring the signals from the rotating sensors to the board: https://www.ebay.com/itm/12-5mm-12-Circuits-Capsule-Compact-Tiny-Slip-Ring-250Rpm-2A-250V-Test-Equip-ED/112240145761

I love the concept.

It occurs to me that if the traces and and SD card spring contacts turn out to be a weak point, they could be avoided by using wires then running the disk for 1 revolution, then running in reverse direction for 1 revolution, and so on. Just reverse disk turning direction every revolution.

That way the disk never twists up the wires too much, but it's not that much more complicated to interpret the data; it's still very what-you-see-is-what-you-get.

you could technically make the movement like a windscreen wiper movement, piston movement etc to achieve that, that way you dont have to contend with back emf from changing motor direction.

I see the tracks as a weak point of this design. You could use magnetic coupling to transmit power (and even data), and optical down the center pivot to transmit data. Just a thought. 

I have seen magnetic coupling for the head signals on an old VCR head.  I would put a wireless module e.g. ESP8266 to talk to the sensor and send out the data on WiFi.

Nice idea & design! Be wary that VL53L0X isn't an analog sensor that you can run at any speed, it has various speed limitations such as how it is only expected to update the data at around 30 times per second, and it spends about 20ms for the distance ranging where it's expected that the distance won't have changed much. So realistically, you can probably only rotate your sensor at very slow speeds (I'm guessing just once per second). You might be better off building a PCB with 20 x VL53L0X sensors (the raw sensor can be affordable if you shop around) that doesn't move. Anyway, I'm sure your current design is good enough for some purposes even if it moves slowly. I hope it goes well!

Why three sensors, and not one or two or four or five or more?  Is there a sampling limitation which dictates how many sensors are required?  Maybe something to do with beam width at different ranges? What is the vertical resolution, same as horizontal beam width?

arguably the easiest geometry to work with in terms of calibration 

So... why are you spinning the sensors and not a mirror?

because you’d need to have a different photoreceiver 

Not really. Think of a polygonal mirror and 3 sensors around it. I think you need a hexagonal mirror to avoid overlap as the mirror doubles the scan angle.

There is a problem  with dead zones, where the sensors block the light path when they look a t 90° on the mirror. So perhaps some overlap could be good, like using a square mirror. Or you tilt the sensors slightly upwards, so they don't see themselves. But then your sensing rays are titled upwards also, except you use a pyramidal mirror (upside down truncated pyramid) instead of a prismatic mirror.

A mirror may also be expensive depending on the wavelength and if partly reflections of the glass surface may distort your measurements...

What about oscillating the Sensor-PCB by (Angle = 360 / Sensors) instead of rotating it? Then you could use cables instead. 

With an L-shaped PCB, you control 4 sensors one on each side of the PCBs. This results in 90 degrees oscillation angle.

Also instead of an octagon, you could also stack 2 L-shaped PCBs. with 45 degrees shift. Depending on your tools, this may be easier.