You ought to write yourself a ticket, that's insane! :shock:
In all seriousness, your GPS is probably fine, it's a side effect of having a poor signal to the satellites. When it doesn't have a good position lock during warm up it will calculate some positions that are wildly inaccurate for a few seconds, maybe more, and during one of those calculations it determined it moved a long distance in a very short amount of time. 300mph is 440ft per second, so if your position error jumped 440ft in between calculations, (which most units refresh once a second) there is your max speed.
Or, at least that is how I understand it to work. I own 4 GPS units of various designs and all of them report some wild speeds on a cold start.