I can't post on this thread anymore, which is unfortunate, so I'm creating a new thread to get this information out there:
For those who were not following that thread, I had a Linksys WRT3200ACM that would start dropping AirPrint/Bonjour packets for no obvious reason. This was causing all sorts of problems on my network, the number one issue being that my wife was unable to print from her iPhone.
The issue was so bad I eventually reverted to stock firmware. Alas while the stock firmware was functioning correctly, it's limitations were preventing me from doing everything I wanted to do with my home network so I decided to give it one more go.
This time I took a different approach. I purchased a used Netgear R7800 off of eBay for cheap and swapped out the WRT3200ACM.
I can confidently say that the Netgear resolved all issues and is functioning as expected, and for the life of me I can't find any difference in configuration between the Netgear and the Linksys devices. I can only conclude that there's either an issue with the Linksys hardware (which I doubt because the stock firmware was functioning properly) or a problem deep inside the OpenWRT plumbing for this device.
I hope this information helps anybody else who runs into this issue. If you can't get it to work, try swapping out the hardware!