I don't know of any 4-ch recorder options in the $500 budget range. It's possible to record mics + SBD through a UA-5, in which case the Ua-5 functions like a mixer. But this option has limitations because you can't adjust for time delay.
You could certainly use a JB3 for recording off the board. You'd just need the proper adapters to get an analog output from the SBD into the JB3. Check the Cables forum for a link on how to do so. Just as the FR-2LE has an ADC, so does the JB3, so you wouldn't need an external ADC.
Since you'd be recording with two different ADCs, and therefore two different clocks, you'd have some work to do in post-production to get the two sources sync'd up. Check the Computer Recording forum for links to info on lining up these different sources.