I carpet boxes all the time (i sell boxes and audio equipment) but I'm kinda far from you and I'm not making the trip any time soon
The 3M spray adhesive that is best is the 77 type. I spray a light coat on the box and a light coat on the carpet as well. Give it a min to get tacky and then put them together. I lay the carpet down on the ground and get it as flat as possible. Then I think about where I want the lateral seam to be. I then start at that point and roll the box onto the carpet gluing each side. At the corners you have to use some exacto knife or scissors skills to get the corners right. It's tough but just takes time. There is an easier way to do the corners but it requires a special box design with end pieces to hide the seams. I've done it a few times and it works well but it take planning before you build the box.
PS: I get my carpet from PartsExpress. I just ordered like 20 yards last week.