Each aspect of your gear chain could use an "upgrade" if you're talking about achieving the best specs, of course... But this isn't as cut and dried as it first appears, I guess.
The AD20 is a fine AD converter, so you're basically just using the iRiver as a bit bucket. The iRiver is 16bit and therefore not IDEAL, but I'm not so sure the 16 vs. 24bit difference is THE critical aspect of your rig. In some ways, if you're being encouraged to switch the mic to phantom and then run it all analog through a littlebox (a great inexpensive preamp) into the iRiver, I could see that maybe being worse than the nice digital signal path you have now. So, as pointed out, you'd need a new deck, too. But that still leaves an analog signal path where you used to have a digital one.
I would think about the potential performance improvements from running that Rode mic off of phantom instead of batteries. As everyone here will tell you, mics are the most important aspect of a rig. I would think that either getting a better, phantom-powered single-point stereo mic, or strongly considering a phantom powered stereo pair, might be better. A stereo pair offers more placement options and greater upgradeability in terms of using different capsules for different polar patterns.
Having a budget here would help, as that would clarify things in terms of what your realistic options are.