Switching over to an ARM based solution is much better than an AVR+RTC chipset solution. Been looking at the STM32F030 chip and it is a perfect fit for this application! It has the following very desirable characteristics:

• 32.768kHz oscillator on-chip. Just need to hook-up the crystal. This might not be as simple as I thought. It has OSC_IN and OSC_OUT for HSE oscillator and OSC32_IN and OSC32_OUT for LSE oscillator. The OSC32 pins are not available on STM32F030 TQFP32 package
• RTC on-chip with calendar and leap year correction
• 8MHz RC oscillator on-chip for running the actual application
• Serial Wire Debug (SWD) based programming using just 2 pins (SWDIO and SWCLK). Need to use the STLinkV2 programmers which are inexpensive ($3 delivered!) on aliexpress
• Works down to 2.4V which is the end-of-life voltage of a 3V CR2032 battery
• 20mA max I/O drive current which can directly drive display LEDs
• Available in QFP32 package. Just enough number of IO needed

Need to use the NDK crystal mentioned in the clocking application notes (page 28). The NX3215SA part is available on aliexpress.

http://www.st.com/content/ccc/resource/technical/document/application_note/c6/eb/5e/11/e3/69/43/eb/CD00221665.pdf/files/CD00221665.pdf/jcr:content/translations/en.CD00221665.pdf

All information for getting started on using STM32 bare bones is mentioned in this excellent article (we don't need no dev boards!) :

http://kevincuzner.com/2016/05/22/dev-boards-where-were-going-we-wont-need-dev-boards/

Or maybe a low power version like the STM32L031 or STM32L051. It works down to 1.8V. Its actually less expensive than the ATMEGA88V (in single quantities on digikey)