Yeah - this is a textbook case where shift registers are appropriate.
32 bits of shift registry, and a MAX7221/19 to drive the 7-segments (it's better than hacking a few more shift reg's together). You could put all those on the SPI bus, and periodically update the display + targets.
Now you've got 15 inputs, plus the pins for the shift registers - which is still too many for an Uno. Since you say the target inputs need to be on interrupts, not polled, I think you might still end up over the limit for an Uno. If you can do it, you'll probably be right against the limit, leaving you at high risk for discovering you need more IO pins later, and not having them.
I'd be inclined to suggest for a 1284 based board (sometimes called "Mighty1284" - Crossroads' on these forums is a big booster of the '1284, and I think he sells Atmega1284 boards too) - it's sort of a happy medium between the affordability of the 328 and the feature-set of the 2560 (as used in the Mega) - or get a Mega.