I think if you draw a distinction between "hired killer" and "professional assassin", it starts to seem less outlandish.
E.g. the former could be just any desperate character willing to do unsavory things for money (or other perceived benefits).. they may be nervous or not, angry or not, talkative or not, experienced or not, organized or not, physically fit or not, local or not, drugged or not, known-to-liz or not... It's hard to rule out pretty much anything they might or might not do without knowing who they are.
The latter is maybe a bit easier to profile but a pretty unlikely suspect.. they're the movie villain with ice in their veins and a personal preference drawn from experience on the type of weapon, vehicle, disguise and ammunition they want to use for a given job. I don't think our best guesses place such a person in tomball that day.