I just finished listening to the ME testimony. I noted a couple of things that were pointed out that I thought were significant.
1. State referring to how she might have been strangled asked if she might have been strangled "...specifically with a piece of wire." ?
2. From previous testimony we have heard about BC doing the famous imitation of Mr. Clean, and admiting to using "warm water and vinegar" - perhaps to mask the odor and acidity of vomitus?
3. State asked the ME if someone were strangled how long to lose consiousness, and how long until death + possible missing head injuries "if there was no break in the skin." or were in the area that has much insect damage. Couple this with the missing sticks. Perhaps she was choked until she passed out, maybe with a little head bumping on the foyer floor. She comes to later and becoming nauseated vomits in the vase, BC hears her and returns to complete the job.
I know, a bit gross and no evidence for it yet, but I am trying to connect the dots in what we know now and how it fits the puzzle.