I know a manufacturer that swears by Pirate Ship. Says it has saved them a lot of money in shipping costs and can also be effective when shipping overseas. I have not yet tried it.
On the subject of upcharges, a large UPS distribution near me recently closed their customer counter so I began using a nearby UPS Store for shipping. I quickly realized that I was consistently being charged significantly more than the estimate provided by the shipping calculator software on the UPS website. This had never happened over the many years that I shipped from the customer counter within the UPS distribution center. When I questioned the UPS Store manager/franchise owner about it, she said they had to upsize the package dimensions or UPS would send them a "surcharge after the fact", not unlike that reported by the OP.
The final straw for me was when, even after I began upsizing my dimensions, the UPS Store wanted to charge me about 50 percent (about $60) above the UPS website shipping estimate for a shipment and, when I questioned the manager/owner to understand why, I was told the address wasn't on the UPS driver's regular ground route. When the counter representative told the manager/owner that it was an air shipment, not a ground shipment, the manager/owner tried to make up a different excuse. I walked out of their store with the package and drove to the nearest FedEx store where the cost of shipping was about half what the UPS Store wanted to charge me, and even less than the estimate from the UPS website. I have not shipped using UPS since.