Thanks again for the input, I finally managed to fix the problem. I guess the guy who they sent out said that I had a lot of incoming and outgoing static? He basically checked that all of the cables in the house were tight, messed with all of the cables outside, then replaced the modem to be safe. Even he wasn't entirely sure what the exact problem was, and basically just did everything he could think of to try and ensure that it was fixed. Happy to finally be able to play games again without waiting all day for the drops to stop!