Plugging your mics into a PFA as is doesn't eliminate the distortion concern.
I see three options...
1) Get the 4.7k mod (costs about $50). That eliminates distortion, but lowers the sensitivity by about 12db or something. Still use the batt box, you would need more gain on the JB3.
2) Get a little preamp like a Church Audio ST9100, or a Naiant Tinybox, and get the mics terminated 3 wire hookup for that pre. This is probably a $200 upgrade, but it handles your gain as well.
3) if you wanted to get the mics wired to phantom adapters like original AT8533x, you might find a pair for $50 or $100 where someone cut them off to make a set of mics wired to a minijack. Now you need a phantom powered preamp to go with them, which costs money.
If you did option 1 or 2, the next upgrade might be to buy another small recorder which has better preamp, like a Sony M10, Roland R05, etc to replace the JB3. The meters will be much better. There is a the Denecke AD-20 which has been in the yardsale for a year, which takes a miniplug, and outputs an optical signal. This would go nicely between the battery box and JB3 if you felt like going that route.