This thread looks very informative for people seeking FTE.

My current situation: I have 6+ years of genuine experience as a developer. From last 3 years I have been working as FT Employee at a stable organization. Form past 2 months, I feel that I am not treated equally in comparison to my colleagues and my salary is not so great for the skill-sets I have. So, I am looking for another FT job in hot market IT hubs like Raleigh, Charlotte or Dallas. I am looking for Direct client if possible. I am looking job sites like indeed, dice, LinkedIn etc and also going through the company's direct website( whatever client I know) but no luck. I did contact vendors like Vaco, Apex, Signature etc for FTE but they told that they have only CTH position. I do not want to go through CTH to have FTE position as I will lose my health insurance and other benefits and I am not confident enough that they will hire me after certain time.

Are there any other reliable means (that I am missing) to get direct full time with client?