16/18 VAC to 5 VDC UPS
You should be able to keep the original batteries, charger and wall wart. This will give you a good 12V rail to work on.

About the 5V rail you can get one of those USB phone chargers for cars, and those should be able to cut it. If you want to roll your own converter go with a LM2596-5.0 fixed buck chip.

As a backup plan, you can use a normal phone charger, a USB battery bank and a 5V supercap to power your Pi continuously.