you know, your horse looks happy and so do you, so don't stress to much about it. Your thigh is so long that actually that 18 inch saddle looks about the right length of flap for you. As you get to know her better and feel more comfortable you will find yourself better able to slow her with your core muslces and will then brace less into the stirrup .
Do some walking without stirrups for a bit to get your leg used to falling further straight down, then pick up the stirrup and try to maintain that angle. It could very well be the saddle does make it hard for you to avoid the chair seat.
That mare looks SO much like the first horse I leased, 15 years ago. She was 19 but you'd never know it. She was a go-go arab, gray, too.