The "sloppy tolerances" won't save you. The brass will take the shape of the chamber and will need to be "full length" sized. I have never used the "Lee loader" but the way I understand it, you can't full length size on it, only neck size (I could be wrong).
If you are seriously considering getting into reloading, I would (since you have an autoloader) consider the Lee turret press, at least. I have one and love it. Not TOO much coin, and with .223 prices today, it will pay for itself in short order.
Best thing you can get is a good book. First thing to get, too. It will give you a much better idea of what will fit you, or if reloading is for you. I think the Lee Modern Reloading is the way to go. It was a great book for me to get started and still the first on I pick up.
su, 2 minis, 2 glocks, buckets of rollies. Lots of Lee. SocomII (SA sucks)