From what I've read numerous times over the years, women typically don't choose violent or potentially disfiguring methods of suicide. They favor poison or the ever popular alcohol-and-pills. Everything about this is just begging for further investigation.
As you say the means -- that is the form of the death -- is suspect. And it is clear that while she did have motive for suicide, others also had motive for her murder. So that leaves opportunity -- have the investigators pursued that?
Probably not.