You said 'no reflective' and downchecked ultrasonic, but would this work?

small ultrasonic transmitter mounted at the tip of each finger

the transmitters 'chirp' in sequence

three ultrasonic receivers mounted appropriately to receive the signals from 
the transmitters

time of flight to the receivers is used to compute the three distances

a little bit of magic math, and....

Bob Ammerman
RAm Systems

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