You can select different sleep modes, with counter enabled or disabled.
You don't need a ATtiny (or Trinket), the ATmega328P as used in the Arduino Uno is just as efficient.
A complete Arduino Uno board is not very efficient, due to everything that is on the board.
A good sleep mode puts the ATtiny/ATmega into sleep for a long time, even if that means that the long time is only 10ms.
Therefor using an interrupt to wakeup is no problem at all.
Everything you add to the circuit, like the 590 counter, needs current to operate. Try to do it all in the ATtiny/ATmega itself.
What about the hall sensor, does it require a current to operate ?