Must just be me. I ship thousands of dollars of stuff (often insuring items for up to $22k to $24k....max is $25k w/ USPS) via the post office in flat rate boxes. I can ship up to 70 plus lbs, and insure for a high value. I nearly always find the post office is much more reasonable than UPS or Fed Ex. Nearly 100% of my items ship that way.
Last year I did use UPS since the customer had to "have it overnight" after a package had not arrived after 6 days, 4 states north, via Priority Mail. (USPS delivered the first shipped item to the wrong address...a marina! It was returned to me about 10 days later.)
Nothing lost or damaged either. (Ok USPS did lose an ounce of gold, but paid me for it!) So, two bad deals in the last 15 years.
If your item can fit into the larger flat rate, that is the way to go. If it can't, then I guess you are going to have to deal w/ another shipper.
I have said for the last 5 years....the only ones making any real money these days are Fed Ex, UPS, USPS, Ebay and Amazon.....cause I am not getting rich selling what I sell.
Best of luck to all. Greg