Well, against very good advice, I stood the corn back up this morning. I weighed all of the options and the soil conditions and decided that was my best bet. Here's how I came to this decision...
The corn is just over knee high. If it stays down, or doesn't get upright enough, pollenation will suffer greatly, reducing the yield. With the corn down, I can't weed it effectively, which is not an option in this garden because of the current pigweed infestation. I looked at the soil and found it to be very wet and soft. Lifting a few stalks revealed that they would stand most of the way up without resistance. So, I made the call. I stood it up until I met resistance, then hilled it in. If I loose the crop, I'm probably no worse off than if I had done nothing.
This was strictly a judgement call. My garden gut told me it was the right thing to do in this instance.