I have two thoughts- the first is to have her nails checked to make sure she does not have some nail fungal irritation because as mschauer pointed out, it is sort of odd for her to straddle the lid like that.
Second, assuming she accepts new litter and you are able to see her standing in it to defecate regularly instead of standing on the lid- you might want to put a cover on the box so the other cat cannot bother her when she is in there. I would not do this unless or until you see that she is ok with the new litter.
The thing about soiling your clothes: I had a cat that would do that too and I also thought she was obsessive compulsive. It turned out she had irritable bowel disorder. I think you might have a situation where she is feeling very stressed and maybe it is upsetting her stomach. The poops may be painful and she may be choosing not to use the box because she associates it with an upset stomach. Or it could just be that the other cat bothering her at the box is making her look for other possible places -or some combination of all the above.
Pooping on your fallen clothes and "moved" shoes probably does not have any significance other than she is finding a spot other than the bare floor and the normal things on it- i.e. places she knows would be inappropriate. I think she is honestly trying to find another "ok" place to poop because she is not liking the box.
The issue to resolve is what does she not like about the box- the litter, the other cat, is she in pain using it (nails/litter, irritable bowel)?
It would certainly not hurt to spend more time playing with her and the other cat equally during this transitional time following the move and the new baby. Cats are creatures of structure and it looks like she is trying to solve some problem on her own. Bringing her and the other cat both back into your world and routine a bit more, to the extent possible, may help eliminate stress for both of them and may be just the thing to resolve this problem in addition to the other changes you are making. The other cat didn't suddenly start harrassing the one cat for no reason, so you would do well to work with both of them right now- regular short play sessions and get them on an even keel.
Good luck. It is great that you are taking so much time to work this all out