Maximizing Battery Life on DA14681

Hello,
We are looking at using the DA14681 or perhaps another SOC chip as part of our very small IoT device in our application strongly limited by battery life. Our device’s mission is very simple: transmit/ broadcast via Bluetooth Low Energy a unique identifier periodically so that a smartphone will reliably discover this signal. We are looking at an advertising interval of about a second with a duty cycle of a few percent. We would transmit for multiple hours and then do nothing for weeks. During our multi-hour transmit cycle, we would ideally turn the SOC off to minimize power, unless putting it in deep sleep is more power efficient. During the multiple week rest cycle, we would turn the SOC off. It would be awakened by another device.
Questions:
1. How Long Does Your Processor Take to Wake Up and Initialize, and How Much Current Will It Draw During that Period? We found from another supplier that, contrary to their data sheet, their processor will take about hundreds of milliseconds or more at several mA to wake up and initialize the RTOS, peripherals, and BLE stack. This means that for their device we are better off putting it into a deep sleep mode retaining enough SRAM to hold the BLE stack between transmissions.
2. For Your Processor, Sleep or Turn It Off? During the roughly one second between transmissions, to maximize battery life for your processor, do you recommend turning your device off or keeping it in one of your sleep modes? If you recommend the latter, which sleep mode is best and how much current will it draw?