In this poem, Dickinson relays metaphorically the possible mental breakdown of a person's sanity. It is a startling poem, and frightening, as she aggressively describes thoughts that incessantly barrage her brain, driving her crazy. She feels her sanity dying, and hence, a funeral for her sanity is the theme of the poem.
As with all poems, the lines are open to interpretation, as long as you can support your opinion with the text. In the stanza that you are referring to, the box could possibly symbolize her former, sane self, that has been put into a coffin, and is being carried away for burial. The box is the coffin, and the creaking across her soul is the noise that taking her former sane self away in the coffin makes on the floorboards of her mind. When she says that they lift a box, she is not referring to herself, but rather to the thoughts that have driven her insane; they are the ones that broke her mind, so it is only natural that they are the ones that take her coffin out to bury her once and for all. That is just my take on it though; your thoughts were intriguing too. But, since she does say "me" and "my" throughout the poem, if she was the one lifting the box, I figure she would say that she heard herself lifting the box, and not "them," which is why I conclude that "them" refers to the they she has been talking about the entire time-the menacing thoughts.
For the "boots of lead", I imagine it is just dramatic effect to indicate how heavy these thoughts feel to her; they are tramping upon her former sanity in leaden boots. That is heavy, crushing, and unmerciful. If the thoughts weren't damaging, they wouldn't being wearing boots of lead. For space beginning to toll, imagine the church bells that toll at funerals; they are loud and somber. But since her rational mind is breaking down, for her, all of space is tolling the passing of her sanity. Everything that she knew in space, is broken, because her mind is broken. The noise must be like all of space tolling, or ringing, at a funeral, to symbolize her demise.
I hope that those thoughts help a bit; it's a tricky poem, but one that is definitely thought provoking. I provided a link to a discussion of the poem that will also be very helpful. Good luck.