how do I effectively market my skill as an independent contractor?

For the past 7 years I have been working for a defense contractor working on customizing content management systems (well known EMC and Atlassian products).

I feel like I have gained enough technical knowledge to be able to independently help other companies or organizations implement their own customizations / requirements. I also feel like I can offer troubleshooting / debugging help as well.

Is it possible to become an independent contractor and work "on the side" and help out other organizations in need of their own content management systems while maintaining my current full-time job? I also hold a security clearance and so I'm not 100% sure what the rules are (like conflict of interest?).

Would appreciate all / any advice from other independent contractors or "small" startups.

In the end, my goal would be to quit my full-time job entirely and essentially start my own company.

I will start by addressing the most important issue first:

Your security clearance. Working for a defence contractor is different to other types of contract work, in that the systems you are working with and the information contained in those systems should be or is of relatively high security concern.

You should actually take time to review the contracts you have signed with these defence companies and see if there are any clauses or provisions that prevent you from doing other part-time work.

Is it possible to become an independent contractor and work "on the
side" and help out other organizations in need of their own content
management systems while maintaining my current full-time job?

As I mentioned above, you need to review your contracts firstly, then you also need to look at some federal laws concerning this too. Doing the same work for other companies part-time could be seen as a 'risk' by the government.

I feel like I have gained enough technical knowledge to be able to
independently help other companies or organizations implement their
own customizations / requirements. I also feel like I can offer
troubleshooting / debugging help as well.

I'm not sure what your skill-set specifically is, so this is a relative situation in which you may feel that you have ample skill, but this may not be the case.

However, you have mentioned that you have been on the job for 7 years, so I assume that what you were doing was good work, as those firms are still working with you for the past 7 years.

The first thing you need to do before branching out, is to actually do some market research. You need to define the most important thing here, and that is to find an actual customer willing to pay for your services.

I don't have experience with either Atlassian or EMC, but they look like enterprise-level CMS software. There probably does exist a market for this, but being enterprise-level, these are probably mid-sized companies who may choose to hire a small team instead of just a single independent worker. Again, I don't know much about these 2 systems, so you should be able to define the target market better than I can (there may be small enterprises willing to work with single contractors).

How to market yourself?

Think of it in terms of "you are the product" or whether you would "hire yourself". In the independent line of work, word-of-mouth is the best referral (in my opinion) and the only way to do that is to create strong relations with clients and deliver above-par work.

Finding clients is the first big hurdle that people face when reading/hearing "word of mouth referrals" but being in the business for 7 years, you must know at least a couple of firms you could do work with, so start from your personal network.