"We have had 4 phone calls today from different people and places wanting us to buy from them...."

Have you followed up on these phone calls?  If not, what are you waiting for?

Like I said, if you don't like the price of this business, get another quote from another business.

Questions I have:

1) How much experience laying carpet does the person who gave you the estimate have?

2) How much experience laying carpet does the Sales Person have? 

I bet I can answer the second question right away...... NONE.

I don't recall reading, and maybe you said it...... how many offsets and odd corners does this area have?  My guess is "enough".  I suspect that is where the discrepancy in yardage comes.  One installer/estimator may be willing to "piece together"; another may just start with a new run. I am not an expert in installing carpet, but that is my hunch.

Like I say...... you have to look at the total cost and decide if you want to buy from this company or get another quote elsewhere. But this company has the right to price however they want.  That is not your decision.

One more thought...... maybe you should just but carpet from an outlet and install it yourself.  You might get an education.