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 Lawn Solution Dual Hyrdo Aerator 24"
2011 Echo(backpack blower), (hand blower), (chain saw), (hedge trimmer), (string trimmers), & (tree pruner)
Craftsman 4.0 edger
2007 Big Tex 4ft metal high side 7' x 12' Trailer
2012 PJ 7' x 16' Dump Trailer
2012 Ecolawn Applicator model 200 Compost Spreader
2012 BillyGoat Force 13 Wheeled Blower & MV650SPH Commercial Vacuum