Adam, why not use a drag mat? This way you will break up the plugs and when the mat gets muddy....it would be easy to clean. I think a drag mat would work very well with your aerator.
Here's a nice one at Amazon.com. The have different sizes...but I think a 3 ft wide by 5 ft long would work amazing!!! And it's only $125.39 with free shipping.
2013 Ford F450 Super Duty Truck
2010 Exmark Lazer Z 60" deck
2012 ExMark 30" Riding Aerator
2011 John Deere Pro Gator 2020a
2011 Lawn Solution Dual Hyrdo Aerator 24"
2011 Echo Handheld (trimmers to power pruners)
2007 Big Tex 4ft metal high side 7' x 12' Trailer
2012 PJ 7' x 16' Dump Trailer
2014 Vintage 8.5' x 24' Enclosed Trailer
2012 Ecolawn Applicator model 200 Compost Spreader