That's awesome! I have only one objection--maybe I just haven't read in enough detail yet, but LH2? I know that most NTRs call for this, but it's volatile stuff--that would need to be one heavily armored core tank, otherwise one pea-sized micrometeorite could blow you right to hell.
In principle, an NTR will run on any fluid, including milk -- the problem is that Isp suffers greatly if you use anything but hydrogen (I think projectrho has Isp values for non-LH2 propellants somewhere).
However, since you are going to Saturn, and you want to stay for a couple of years, then you don't need to take return propellant -- because you will have a lot of ice available (all these moons are made of ice!).
You can also go jet-setting between the moons: after you land, load up some ice into the electrolysis module (bimodal NTRs double as power plant!) , and you are good to go for the next moon. You can also use produced oxygen for breathing. Or water for drinking / sanitation. So you need to take less water from Earth, which means less mass.
If I was designing the mission, I would never start with Iapetus, because it's out-of-plane. I would first go to a relatively small in-plane moon, refuel, and then go jumping around. Can also use Titan for gravity assists. Titan landing... um, it's a different pair of shoes. I think you need wings. On the other hand, you can land on the shore of Kraken Mare and just suck liquid CH4 into your tanks without electrolyzing stuff -- NTR performance on LCH4 is decent IIRC.
If you have water, then you are only limited by the fissile stock inside the reactors and the endurance of the engines -- these can be made arbitrarily large (within reason); the NERVA/ROVER program logged hours of combined burn time.
Better yet, switch your NTRs for
LANTRs, at least in landers. Then you can trade thrust and Isp as needed. Sweet thing for landers/shuttles... Look for Stan Borowski's papers on NTRS.
One more thing... NTR stage disposal on returning home (you don't want a hot NTR core to enter Earth's atmosphere, because it's a Chernobyl-level contamination). The way it's normally addressed is that you do a hyperbolic Earth encounter, the crew transfers to an Orion or something like that, separates, and does a correction burn to aerobrake. The actual spacecraft zips past Earth on autopilot, then does a burn to raise periapsis to 1.1 AU. Another option is to crash it on the Moon, although that significantly complicates your encounter planning.