Indeed if the dimensions on the slip were not included in the first quote, that is why the price went up.
Anything that has a single dimension over 12" drives the price up.
Go to the USPS site and punch it into the calculator, there is a choice for your box and it has the 12" limitation for one of the selections.
That package may only weigh 4 pounds, dimension weight is closer to 16 on FE if I had to guess. What does an 16# package cost to ship to that location? I see that it says 13# on the receipt.