I found that most my OTTB's liked being work 5 days a week for short periods (30 - 45 mins) rather then only 2-3 days a week for long rides (over an hour) I also do a lot of transitions, just make sure you stay soft because if you pull they will just pull back. You need to teach them about your seat and legs.
As far as the right lead .. I have never really had any big issues with it .. both leads are a little fast and unbalanced. Everything will take time ..
5 yr OTTB gelding
5 month old TB/Morgan Colt