Goggins also does 1,000 lb rack pulls like its nothing.
I don't think its so much about how much you lean as it is about where the weight is balanced. It seems to me like you get on your toes (which is EXACTLY what I do) and it just makes the lift harder. I really don't care about the lean so much as the distribution of weight, which to me seems to transfer to your toes about 1/4 to 1/2 way up. The only way I fix this is by finding that spot about 20 degrees up to stare at while I lift. It also helps block out any distractions while I'm lifting.
The hand placement thing for me is also about head position. If I bring in my grip on the bar I have a natural tendency to jut my head forward. My chest follows my head. I'm also able to build a nice tight shelf and get comfortable by pulling my shoulder blades together hard. I wouldn't try changing your grip until after meet, but the head cue may help.