With suffocation they can trace what kind of pillow was used by checking her airways for fibres. From there they would likely be able to check if these pillows were kept in the home (I don't know about other people but my pillows are all the same brand). Then they could test those pillows to find which one was used to suffocate, check fingerprints, etc.
I've just realised that they haven't mentioned that they are looking for a murder weapon. So my guess would be that it was something that was done without a weapon. My guess is that drugging, strangulation and suffocation are the likely causes. Unless I've missed something.
That is a very good point about lack of search for a murder weapon (not reported anyway). I agree with your possibilities - also, my initial thoughts right at the start were that he perhaps pushed her and she hit her head on the concrete (this can be lethal if unlucky) or hit her head on the edge of a coffee table/furniture. To be honest he just doesn't strike me as a violent guy, which is why I guessed these scenarios, but I am not an expert, I don't know him and impressions can be deceiving.
If it was an accident such as I've suggested though, I just can't fathom why he wouldn't just call an ambulance though. Why try to cover it up?