I always use a credit card. Anything you charge you get a receipt for it. I take a zip lock sandwich bag and my wife and I always put our receipts in that zip lock. Each day, I will check our charges via the t.v. and if there's something I have a question about, I simply look at the receipts--I've never been charged for something I didn't get and have always gotten the final bill around mid-night or a little after on the last night. I check it first thing the last morning and always know almost to the dollar what it will be before I even get it.
I hope you get it worked out and feel that if they were so quick to make a mistake , they could be a little faster than 6 weeks getting it corrected for you.