While in general direct TC applications are more competitive than VS applications, I think you should go for it. I know people with similar levels of legal experience who managed to secure TCs in this way - perhaps partly because most people concentrate all of their applications efforts in the VS cycle and ignore summer opportunities, thus making them comparatively less competitive. Just make sure to select firms that are know to recruit substantial numbers from the direct track and ideally ones who do not explicitly state that they expect applicants to have substantial legal work experience.
Finally, although this is slightly unrelated, if you find yourself starting another VS applications cycle next year, I would definitely advise you to target more than 8 firms (unless you have very specific practice area interests or time limit issues). I think the "it's a numbers game" saying holds to some extent and that you therefore want to submit as many high quality applications as possible.
