I think I should have enough power, as I've put an ampmeter in-line and the most I've seen pulled (when it's working using the 3v3 external supply) was 50-60 mA.
Any ideas what I might be doing wrong? Something wrong with connecting the MCP1700's? Something else I'm missing?
Your problem is not the quantity of power available from your supply, but rather the quality.
In short, your power isn't clean enough. You can try adding some additional filtering (an electrolytic, at least 10uF and maybe more -- up to 470uF, depending on how noisy your power supply is.)
The 1uF caps are consistent with the MCP1700 data sheet, so that should be fine. The 0.1uF across Vcc and Gnd near the module is also a good idea. Just add a nice fat filtering cap to reduce overall ripple and noise and see how that works.
Getting the power supply correct for the nRF2401+ modules is often the hardest part. When they are supplied correctly, they peform very well, but they like their power clean, clean, clean.
Let us know how you go.