Arthur,
Were those plating wires used only once or were they used for multiple cycles? If multiple cycles, there could be alternating layers of nickel between the Rh layers. You said you got higher yields with nitric than with AR. Maybe all the Ni wasn't leached out with the nitric, whereas it was with AR. If it wasn't real hot, that could happen. Test the Rh foils from the nitric with a good magnet to see if any Ni is present.
If they are gold plating also, there could be some gold layers there that aren't touched with nitric but are dissolved with AR. In this case, though, you would probably see the gold color.
If some Rh is dissolving with AR, maybe you can prevent this by diluting the AR a bit with water - say, 25% water. Even dilute, it should still quickly dissolve the Cu and Ni. Play with some samples.
Were those plating wires used only once or were they used for multiple cycles? If multiple cycles, there could be alternating layers of nickel between the Rh layers. You said you got higher yields with nitric than with AR. Maybe all the Ni wasn't leached out with the nitric, whereas it was with AR. If it wasn't real hot, that could happen. Test the Rh foils from the nitric with a good magnet to see if any Ni is present.
If they are gold plating also, there could be some gold layers there that aren't touched with nitric but are dissolved with AR. In this case, though, you would probably see the gold color.
If some Rh is dissolving with AR, maybe you can prevent this by diluting the AR a bit with water - say, 25% water. Even dilute, it should still quickly dissolve the Cu and Ni. Play with some samples.