steering
Except in cases of current shear-which is basically moving from one body of moving water to another, current will not affect your steering. The boat simply moves in the direction of the current at the speed of the current.
As for the rest of it, yes, you CAN change direction by moving around the boat. If you are balanced annd sailing along, then moving forward should make you head up, moving aft will make you bear away. Moving to leeward will also head you up, to windward, bear off. The more weight that is moved the greater the effect.
As for the self steering on a broad reach, if when you tie things off, the boat wants to bear off (as you describe), then tighten the main and ease the jib slighty. The best thing is to experiment securing the tiller once you have boat close to neutral. Once that is done, adjust the main and jib until the boat goes straight for a while by using those methods (main in/jib out to head up;main out/jib in to bear off), you will find an equilibrium somewhere.
HOWEVER, as soon as there is a change in wind speed or direction, the balance is changed and you must readjust! Maybe this is what happened.
Think about it like this: You get it all sorted out, go below, and the wind increases. If no trim changes are made, the boat will head up. If the wind decreases, it will bear off (under the same trim).
This been explained in great detail in previous posts, but if you have questions feel free to post 'em-I'll answer as best I can.
BTW-I also love the name of your boat!
Seth