Chaining two batteries to achieve a specific voltage range under their maximum
This arrangement will not work at all, not even for a short time. 

The CR2450 battery (per Sony, Panasonic datasheets) has a drop of ~100 mV with a load of 7.5k, or 0.4 mA. This means that the internal battery resistance is about 250 Ohms. Even if you try 4 LEDs at 2 mA each, the voltage will drop by 2-3 V. Your Attiny will eat another 1 mA even if you run it at 1MHz. The main killler will be DM7495 with typical consumption of 50 (!!!) mA. Two of them will take 100 mA, plus 17 mA for NTE74LS164. There is no way for these batteries to deliver 120mA, the short current (voltage drop to zero) will be ~12-15 mA.

So scrap your project and start over, with CMOS chips as Kevin suggested, and a different battery.