Franc's idea may still work. It will be easy to discriminate signals that don't arrive within the necessary time window to be valid targets. I think optical methods may still be best, maybe a webcam mounted off axis is all you need. One problem though depends on the calibre you are using and the ammo - the size of hole you get.

Do you want automatic scoring or just some way of relaying a picture of the target to a scoring desk where the scorer can use a mouse to click on the centre of each spot on the target. He clicks say three reference spots on the image and that calibrates the scoring ?

Steve