Yep, that seems like the order I found the upgrades. I went down, then to the left, up and round to the right, down then back up for the last upgrade.
Moving the boxes was alright, though a little clunk at times due to needing enough space to pull the 'rope' but in most cases they weren't much of an issue. Overall I felt the cases where you needed to drag the boxes to use as platforms felt more interesting than when you only have to pull them out of the way.
As for skips I noticed a room with 3 boxes up on the left ledges, it seems like if you could stack all 3 then drag them to the ledge you could get up without wall climb. Tried a few times but couldn't find a way to drag the top most crate off and have it land on the other 2 crates.