Good report. My situation is somewhat similar to yours.
You mentioned a time conflict between cold approaching and managing your existing relationships. However, I would look at this as an advantage rather than a disadvantage. Here's why. When you're single and horny, you can't help but approach women from something of a value-taking perspective. It's hard to have a true abundance mentality in that situation (if you're getting laid several times a week through cold approach or online dating then that might be different, but let's assume that isn't the case). Whereas, if you're getting laid regularly with your gf, then you're approaching women from more of a value-giving mindset, or at the very least an outcome-independent mindset. This can be a little bit bad in some ways (you don't commit as fully to the interactions), but is a very useful exercise.
The other thing to look at if you're concerned about a time conflict is this:
http://www.sashapua.com/how-to-defeat-approach-anxiety-forever/
I recommend this article to someone every week (most recently Smith, due to a problem he described in his journal), because it is awesome. Once you master the suggestions in this article you'll basically just integrate approaching into your daily routine. The only reason you're not already doing that is because of AA.
Mind you, I'm not sure what would happen if you tried to put Sasha's recommendations into action without first being comfortable with cold approaching. I think it would probably work, but it wouldn't hurt to set aside some time specifically to cold approach in the beginning, because it will be easier to build momentum and to keep yourself accountable (you set a target that you'll do 10 approaches before going home... I rarely do anything like this anymore, but it
was helpful)
Ray