Welcome back! Another Asura person here, look me up in game (same name in game as forum). I run non-Aby parties and do lots of non-Aby stuff. I've got a pearlsack for a non-Aby Linkshell of people who basically run parties away from Abyssea and another pearlsack for a 'general' LS, which is social and orientated for people of all levels and has quite a few members (it's also very friendly, nobody stands for infighting or douchbaggery). So you don't need to rush and I'd be happy to help you out with anything you need. In the way of parties, I run anything from Valkurm Dunes to Whitegate.
I'm always willing to help people out, after all, there were people who helped me out when I started.