I don't know why I didn't think of this before, but it has totally solved the skipping issue on my end.
It only works if you use a player OTHER than Live365 though.
I use MusicMatch and it occured to me they must allow you to set your cache size.
Sure enough, there is a setting for that to eliminate the buffering problem. By default it was set for 250 mb or kb (don't recall which). I upped it to the max of 2000 and haven't had a skip since!