hmm... may be a shot in the dark, but SYN flood (or something similar) may actually be in play here.
It seems like your ISP's modem/router may be running as a simple pass-through device. I hate to even suggest it, as it would incur additional expense if it is the fix, but see if you can get your hands on a router that has an SPI firewall on it. Most any you pickup new at Walmart or Best Buy and such should have it (don't think you can find a Linksys or Cisco without it these days). Chances are, you may be able to borrow a friends router if they're using one.
The reason I suggest this, is the SPI protection built into the router is basically designed to drop all server connections not initially requested from a client behind the router. In theory, it would only let in the traffic coming from the servers you have already established connection with first as an outbound request from your private network behind the router. You may find you don't even need to use port forwarding also. I have never had to do it in over 7 years of playing the game--and I don't use PnP port forwarding either. Both myself and my daughter can be tooling around on our laptops and/or the PS3, while she face-times or tinkers on the web with her Ipod Touch over the wi-fi--and I have no problems with FFXI and no ports are forwarded to my PC. That's like 5 or 6 devices using the internet at once, and I've been using the el-cheapo's from Wal-Mart and Office Depot (my current Linksys is on clearance at Walmart for $20). I've even run uTorrent with a dedicated port-forward to it for seeding (it's the only time I actually port forward, just for torrents).