Distance Measurement - between 6 points, individually moving in (almost) any direction within 1m
You may try to implement some kind of ultrasonic transponders. The
emitter sends a code addressing a specific receiver. Upon recognizing
its address, the receiver replies after a short, fixed delay. The
emitter measures the time it took the response to reach it, and from
there computes the distance.

You may need some kind of omnidirectional transducers (e.g. this
models) if you want the measurement to work in any
direction. And also a protocol to avoid several emitters talking at the
same time.

This seems to me like a very complex project though.