Thanks for the replies, I'm fairly certain the non-moving pad is set correctly. I'll try bedding the pads this evening. I disassembled the rear calipers and couldn't find anything mechanically blocking the brake.
It appears the front/rear sets are interchangeable, so I'm going to try putting the front calipers on the rear rotor.
If that narrows the issue down to the calipers themselves, anyone have any caliper recommendations? Primarily looking for good value, don't need anything high performance.
The cable brakes that everyone seems to like the best are Avid BB7s, which have been around forever. They are more adjustable than the cheaper BB5, and there shouldn't be much of a price difference. Either will be compatible with your current brake lever (or any V brake type lever).
I also suggest checking the cable and housing for any kinks or rust that can affect braking - but that's more just maintenance than something that would cause the lack of braking power that you're describing. I like using full length cable housing if possible, because it pretty much seals the cable from water getting inside the housing and rusting it.
Another cable brake setup tip: if braking feels spongy at the lever, you can try setting up the brake such that the caliper arm is partially pulled even when the brake lever is fully extended - - difficult to describe, but basically set up the caliper with the cable a little "short", such that the caliper arm is already pulled a little even with the brake lever at full rest. Hope that makes sense.