Rebooting your modem will reassociate you with a different IPGW sometimes.
Each service plan for a particular Gateway/beam will have a set of IPGW's that it can use.
You mean that ground based infrastructure is causing these problems? Wow, just wow. How is that even remotely acceptable? Beam saturation, ok, they over sold, but anything else that doesn't require a space trip to resolve is just bad service.
Probably not exactly a ground based saturation issue, there are far more things involved with IPGW associations, such as frequency ranges the satellites use.