This time of year, winds along that route at KA altitudes (upper 20s through low-mid 30s) are probably going to average in excess of 75kts...with many times well north of 100kts. Even flying a 200GT or 300 with cruise TAS of 300kt+ there will still be many times where your groundspeed is down in the 170-210kt range.
Cook @ KBMG has cheap fuel if you need a quick intermediate tech stop...