Moving company charged me twice of the quote. Is there anything I can do?

Location: NJ

I have moved quite a few times recently in the last few years between college and the traveling I need to do for work. I’ve been sick of all of the packing and transporting everything in my car so I wanted to look into a full service moving company and now I’m wondering if I’ve been screwed over by them. This is a moving company and not a broker. I’m currently looking through everything I have to find if the quote I had was binding or not but I believe it was.

I spoke with the salesman over the course of a month or two asking plenty of questions after what he originally quoted me at 500cubic feet when I listed everything off the top of my head. I was very suspicious at this because my dad and I packed a 1200 cubic foot truck nearly to the brim when we moved me originally. I found videos of my apartment I took before I left to make sure I left everything as I wanted to. I was away from my apartment for work at this time and the only belongings I had with me that weren’t in the video were fit into my car. I had my car packed even more full than when I moved than when I came back home. I sent him the videos of my apartment and he quoted me at 650 cubic feet ($3800). I asked him if he could give me a higher one to add more cushion and he gave me one for 700 ($4100). In these email chains he was very adamant about how much professional movers could packing things together tightly and that I wasn’t going to need that much space. I believed in his professionalism and trusted him with the other pieces of advice he gave me. I expected maybe \~1k extra after everything in case there were boxes or anything else I might’ve forgotten or not known about with professional movers.

During this time I was comparing the costs to pods or renting a truck again and flying one of my parents out to help me pack. Flights were stupid expensive the week I needed and I felt like the hassle of everything wasn’t going to be worth just having someone else do it for only the $300-$1.3k price difference that I estimated so I decided to go with the moving company. One of my questions was what would happen if there was more or less space that was used and he said that I would just be charged at the same constant rate and they just change the cubic feet in their calculation and added a little bit extra for fuel. That being said I signed with the 650 cubic feet quote because I trusted the professional.

Yesterday they took everything from my apartment. It ended up being 1100 cubic feet and the cost went from $3800 to $7600. Some misc costs were included that I was ok with, like I didn’t realize everything needed to be in a box and that was priced fairly, but there was a LOT of extra money because the estimate he gave me was vastly different from what the movers packed. I watched them pack and there was a lot of space inefficiencies but I didn’t want to tell them how to do their job. I suggested something that my dad and I did when we moved me previously and they said they couldn’t do it that way because it wasn’t sturdy enough. The only indication I got was after I signed everything and one of the movers told me it was probably going to be more than 650 cubic feet while they were packing everything up. I didn’t know the final cost and numbers until everything was packed up into the truck and it was closed.

Is there anything I can do in this scenario or am I just screwed out of an extra $3800? I was misled and I’m going to call the salesman who I consistently spoke with before but I don’t know what to say. My dad told me when I go to pay the second half I should use my credit card (I didn’t before because it s a 5% surcharge) and then dispute the charge but I don’t know if I have a valid enough case. I would have gotten a truck and done everything myself if I knew it was going to be double the cost but I don’t know if I’m too late to do anything. In my brain because their rate is based off of cubic feet it went how it should’ve but it’s just the fact that he was telling me 650 cubic feet would be more than plenty space. I have evidence of this in an email chain along with the videos I sent.