I think I have a similar mindset. I like independent work, but I find that I am more motivated when working with others. However, I don't think that will hinder your ability to show that you are an independent researcher. As mentioned by @aeismail, the defining point of independence is that you are able to generate and pursue your own research ideas and agenda. If you do it alone or with others is irrelevant.
In a lot of cases, like when you applying for positions, etc. You will have reference letters to accompany your CV. Thus, the author-list is not the only place to show your independence. In the letters your coauthors and mentors can attest to your independence.
A research statement or cover letter also is a great place to highlight your independence. If you work with lots of different people, then you can show how all these projects tie into a broader theme which is distinctly your own. In computational science it could very well be a theme like "I like developing information theoretic explanations for neural and multi-agent activity" and then work with an auditory group, a cognitive group, and a population biologists can be great supporting evidence of the fact that your ideas and approach are unique and independent, not to mention widely applicable.
Taking a leadership and organizational role is another clear way to show your independence. A personal example: I prefer to read and discuss papers with others, so I organized a reading group that meets weekly (ideally). A bit of my time gets consumed in organizing and managing this group, but it is more than made up for by the extra motivation I get to stay on top of the literature.
As for the atmosphere; group-work is not an antithesis to academia. It is very important to show that you 'play well with others' and frequent collaboration is a great way to do so. Especially with the large push for multi-disciplinary work, being able to work with people of various background is a great asset. Further, as a faculty in a research university, one of the things you will be expected to do is supervise and teach students. This means you need experience in sharing and developing your ideas with others, something that working in isolation does not nurture.