Base on the block diagram, the output of the PicoUPS-120 was not fix at 12V, it can be 21V when using your 15v torroidal transformer or 10V to 14.5V using SLA battery.
Your 15v torroidal transformer which output 21V was way to high for the PicoUPS-120 which have a max of 18V
Use Buck-boost switching regulators. They will maintain the desired output.Step-Up/Step-Down Voltage Regulators
Buck-boost and SEPIC converters work with input voltages that are higher than, equal to, or lower than the regulated output voltag