Moving is your Search the List category to find well-rated and reviewed moving companies - though normally they require 4-6 weeks advance notice during the prime (summer) moving season, so you are cutting it tight on this.
You can also find some moving tips and some opinions on specific interstate moving companies in the Home > Moving link under Browse Projects, at lower left.
Based on performance I have seen and heard of recently (we are in an area with lots of mobility, and a couple of family moves) - if I were making a long distance move at this time, personally I would go with Bekins or Allied (though don't believe Allied's web tracking of your shipment - seems it is a couple of days behind time so your shipment can arrive before they say it is anywhere near to you.