With that much power a boost converter would allow your +5 volt "limitation" to work with a lot of different amps....
Here's a thread to give you some ideas:
8 volts is a little higher then I expected there but it's OK.
Sounds like it would be good idea to check and re-adjust (if needed) the PSU voltages when you get the new batteries in your good meter. Anyhow...
What's the DC voltage reading between the lead sticking out of the top of L1 and ground?
(should be 3.3 volts)