My question is if I were to up the power supply from the 220 watt that it comes with to a 300 watt would the GMA X4500 be able to perform better?
The GMA X4500 performance will be exactly the same. Changing PSUs will have no effect.
I did find a 300W SFF PSU FSP Group FSP300-60GHT 300W TFX12V
The size is 3.35" x 2.76" x 6.89". How accurate were your measurements?
It might be a good idea to cruise the Gateway forums and see what other SX2800-01 owners are doing for upgrades.