Here's my situation, I run a couple of lightweight spinning setups for catching schoolies from the skiff, one with 6# fireline and one with 10# fireline. I usally tie all of my setups with a bimini and then use an albright to attach my leader. With these lightweight setups I was having problems with wind knots, especially from the double line of the bimini. So I've been using a uni-to-uni, doubling the fireline, to attach leaders of 20# fluoro, but this knot gets real beat up going through the guides and the other night I had both setups fail on me with fish on. Does anyone have any thoughts on what I can use here? I thought about using an albright but wasn't sure if I could cinch it up correctly with just a single strand of lightweight fireline to pull on.

I use the albright and the slim beauty and have never had a failure with either one.
check it out.
http://www.midcurrent.com/articles/knots/slim_beauty.aspx

Keep your bimini short, tighten the unies in stages (firm up each, slide together firmly, sock down each, then sock 'em together hard...if they slide more under a load they pop). With 10lb fireline (which is under rated) on small rods (where 10lbs of drag isn't an issue), I've done OK just using a carefully tied uni-uni in the single lines. Wouldn't trust one in 6lb (nor with mono-mono) however. Be careful that the first wrap of the bimini.

Also, the unis need to be socked down as tight as you dare if you intend to trim them very close. Otherwise the knot can push a wrap off one end and everything fails.

Blood Knot. No double lines , use Ande for a leader. Your running line is pretty light , even for schoolie fishing IMO.