I carry a Vertical shoulder rigged Blackhawk on my left side, under my pinned on shoulder and a Hawaiian shirt.
I walk with a cane, meaning my strong hand is usually filled, but I do practice both cross draw, and the "Prairie Twist" same side draw, and I find that my weak side draw is actually a touch faster than the full reach across (shorter trip)
As to flagging people, the cross draw does indeed leave you widely sweeping everything to your left, but the twist mostly aims down and a small loop to the side, before coming up vertically at the end.
Practice, practice, practice.