Just a word about the UPS controller for this project.
The core "brains" of the UPS is an full ups system IC PN: LTC4040 from Linear Technology/Analog devices.
This device is the "Cadillac"** of UPS controllers.
What I appreciate most is the ability to limit battery charge voltage. By reducing the charge voltage a little power is lost but is much better for the battery life. All the other battery charge IC's charge Li-on to the battery max of 4.2 volts. Then they hold it there for basically forever (as long as input power is present). This is a worst case operation for a Li-ion battery.
Other leading particulars:
- Step-Up Backup Supply and Step-Down Battery Charger
- 6.5A Switches for 2.5A Backup from 3.2V Battery
- Input Current Limit Prioritizes Load Over Charge Current
- Input Disconnect Switch Isolates Input During Backup
- Automatic Seamless Switch-Over to Backup Mode
- Input Power Loss Indicator
- System Power Loss Indicator
- Selectable Battery: Li-Io(3.95V/4.0V/4.05V/4.1V) or LiFePO4 (3.45V/3.5V/3.55V/3.6V)
- Regulated charge current
- Low battery shut off
** this may be a dated reference 
John