The other thing to consider with your approach is that, irrespective of the number of analogue inputs, there's only one ADC, so getting around all (say) 16 is going to take more than one and a half milliseconds.
I once saw a "live fire" tactics trainer that used a laser in the handgun barrel, triggered by the flash and shock of a blank round firing.
The target(s) was a vest, woven with a mesh of "leaky feeder" optical fibre, which was capable of registering hits with a fair degree of accuracy.
I didn't ask the price.