There is no 5V battery system??? The term 3V and 5V boards has to do with the processor voltage requirement. Not the battery. How the board handles the battery is a separate issue. PS-1 does have a 9V ish regulator and the battery seems to send it's 8.4 V to the PS-1 processor. There are 2 regulators.
PS-2 5v I was told uses a circuit to reduce the 8.4V battery voltage for use. (I have not really studied PS-2 5V circuit).
PS-2 3V boards have a 5V regulator, and a 3.3V regulator. The 2.4V battery is charged from the 5V regulator. The 3.3V regulator is powered by the 5V regulator. They use an inductor to kick the 2.4V battery up to a 5V value to drive the 5V regulator and hence the processor.
If you measure the battery terminal output with a battery connected you will only see about 2.5-2.7 Volts depending on battery state. If you connect a BCR it will charge up to 5V+ value. Hence using BCRs rated at 5.4V. The inductor circuit isn't needed to boost the battery source voltage when a BCR is used and track power is turned off.
So bottom line is use a BCR voltage rated to the battery value you are replacing and don't worry about the details. While the 1.5F rated work, I tend to choose the 2.5F for the PS-2 3V. Slightly longer to charge but does have the capacity to handle prolonged shutdown of some of the sound sets. As long memory can be recorded at shutdown, no worries. G