|There's not much you can do directly since the issue is on the internet.|
What you're describing is the difference between being online during peak usage hours and non peak hours. During peak usage there are many more people active online than during non peak hours. This is why your ping times get larger duing the peak (busy) periods.
I won't go into details but if you're curious, google "contention based networks" and "CSMA/CD".
I would say avoid gaming during peak hours is about all you can do.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.