I'm going through the EXACT same thing with North America Transfer out of Simi Valley, CA. They more than doubled our moving bill AFTER they collected our things. Now, my wife and I are stuck trying to figure out what to do, as we have some really important items that are in their possession. We were quoted $1275 and now they want $4500. Called FCMSA and AMSA who are both trying to help, but we're seriously consider telling them to keep our sh*t and not fork over another dime on sheer principle alone. Who knows, they may never show up anyway.
If anyone has any experience with how to avoid being screwed, please let me know!