That won't be the guy. I am making a prediction (actually repeating what I predicted yesterday) that it will be an animal care technician that works in the animal facility in the basement of Amistad. Everything fits, all of it.
We know that's where she was headed at 10AM. He would be very familiar with the area, especially with where the body was placed. He would have access to the facility. He would have seen her every time she went there to work with her animals- they may have chatted occasionally and she would not have feared him. He would have had access to a locker room/shower and multiple sets of scrubs, since you do not wear street clothes or lab coats for that work.
I believe he finally approached her, it went badly and he killed her during the struggle. It was a small amount of blood on the "clothes" maybe it was his, or she had a nosebleed. I am guessing he strangled her in a panic to prevent her from screaming and alerting other techs in the facility. Hid her body in the nearest possible place, took a shower and changed, hid the scrubs in the ceiling and clocked out at noon for lunch.
I am familiar with these facilities, so I am thinking I will not have to eat too much crow!!