BobG said:
...Trying to balance 50/50 on both legs is exactly what happened to me.
What is the correct way to "tilt slightly toward the uphill side as you roll toward the stop"?
As you're arriving at the stop line, just before you are actually stopped, just lean a bit. It doesn't take much, just a tilt of the head or a slight shift of the upper body. Once you're thinking about doing it, it'll sorta just happen. Even just putting out the leg on the uphill side will do it.
You can also try practicing on level stops; at one stop try leaning left and balancing only on the left leg with the right foot on the floorboards, at the next stop keep the left foot on the floorboards and rest on the right leg, etc. You'll build up your leg muscles a bit while you're riding; not a bad way to get a little exercise, eh?
Keep in mind that it's only a slight lean; just enough to keep the bike from tipping the other way. Too much lean and you'll suddenly be trying to hold up several hundred pounds of bike on one leg.
HTH.