Sorry about slow answering to this topic, but my 6 months old kid takes up almost all the free time. Earlier I tested cutting the mods to 50, then the byte count reduced to 65536 from the 131072.
Then I started to remove mods, but got down to 45 until my kid woke up. Still the same error.
I have pure Forge server and use the normal launcher, I even tried tampering with my routers settings couple days ago when I tried to get my server running again in 1.7.10.
Here is a link to my dropbox containing my mods folder. https://www.dropbox.com/s/lo6ei2ady1tgyei/mods.zip
I'll see if I have time to send my logs. But basically those are the same as the topics author has posted. IOException 65536 bytes in packet 63 and after that the logs display random Bad Packet IDs
Ninja edit: That is the mods folder from my testing sessions... So there are more mods in the pack I have been using earlier when the errors started. I can post the full modpack if needed and try to provide my logs too.