Back in the day, I used to sidress soybeans with a 2000 gallon tank that could get between 36 inch rows.  The tank had two knives that ran in the wheel tracks.  They threw a lot of dirt and would have knocked small corn down.  The window for doing this with corn would have been very tight.  Also, you can't get much done with a 2000 gallon spreader.  The DNR would frown on the application to beans as well.

I think you need to get the manure on first.  I've had good luck with late spring manure applications followed by early season corn.  Maybe you could do something like that on a few acres if there is an early season hybrid you can plant.  I'd think in your area you'd do OK with a 100 (edit: or perhaps later) day hybrid at the end of May on a few acres.  If you have some early hybrids in your planting intentions, save them for this purpose.

Somewhere on here someone posted a link to a video of manure being sidedressed in corn with a drag line on a huge reel.  The reel would unwind going out and wind back up coming back on each round.  It looked like an expensive rig.