When second crop hasn't been cut, we've payed to have combines come harvest wide strips by the blinds and haul it away, so we could legally roll the stubble in that part of the field to open it up and leave the standing (and eventually falling) feed in the rest of the field. But while you would think the birds would be drawn to all that flooded grain, our results have been mixed, depending on whether geese take the field. If geese get in there and knock down a lot of it, ducks will follow suit and use what they've opened up, but they seem more attracted to the open water than the standing rice. If geese don't knock down the rice, it gets surprisingly little duck use. And that's with grain present and not just plants that probably won't head out due to colder temps. So in your case, I'd definitely want to roll it all and count on the open water for draw.
If you think I'm wrong, you might be right.