Best way to charge 750mAh in portable device

I know there are many posts on voltage regulators in battery powered applications but I hope to gain a better understanding of my specific problem.

The portable device I’m working on charges a li-ion device at 750mAh 500 mA (charging current) using disposable batteries. The solution needs to use consumer available batteries and the device will be used in a remote area without outlets so needing to charge is inconvenient. Also a small form factor is desirable. I only want to use a separate li-ion and rechargeable batteries if there’s no other option to reduce complexity.

My first solution was using 4 aa batteries in series and a switching buck regulator to charge and power the components at VCC = 3.3V. I am aiming for 8 hours of use time. I know more measurements would help but I have none right now.

My plan is to have confidence in the approach and then take measurements and optimize. If anyone experienced could help me out that would be greatly appreciated.