If you're going for lower group stuff, perhaps talk to some GA operators and even just ask if you can work with them for the purposes of logging SOE hours. That'll also give them a chance to see your work ethic etc. and they may even offer you a job once you get your license.
I'm currently employed in the industry but am hitting the same kind of obstacles you are: everyone wants LAMEs, but no one wants to spend the coin to train them and give them work for them to build SOE hours. It's a catch-22.
Cheers,
John