Efficiently reducing input voltage
I'd simply replace your TPS63050 with TPS62745 or TPS62056 which support your desired input voltage range.

An alkaline battery has a best-case self-discharge rate of about 2% per year. On a 2000 mAh battery this represents 40 mAh/year or a continuous equivalent discharge current of 4µA.

Therefore having a standby current as low as 100nA is unnecessary. The batteries will be dead and corroded long before a difference between 100nA and a few µA is noticed.

If this is about extending battery life, then a linear regulator would be useless, and optimizing the DC-DC efficiency when the circuit is drawing 150mA might be a better option, although that depends on the duty cycle.

For example if it draws 150mA at a 0.1% duty cycle, this corresponds to 150µA average. An efficiency gain of 1% on this due to a better DC-DC or component choice will be 1.5µA which would swamp the DC-DC's idle current. So you have some math to do. Depending on the duty cycle, the DC-DC with longest battery life may not be the one with lowest idle current, efficiency is important too.