What exactly does riding on a loose rein achieve, except showing a horse's realxation at the walk? Riding on a loose rein in a trot just teaches the horse that contact is not important and does not actually need to be established at all times. Even in a "stretchy circle" a horse should have contact with the bit and be reaching over his back into the contact.
Sorry, that's my biggest pet peeve :)
As for you, you seem to have a fairly solid position. In the rising trot you tend to have a "cheerleader back". You need to focus more in the rising phase of the trot on letting the horse lift you out of the saddle, putting your leg on and keeping your back flatter. Your thumbs also need to come ontop and your elbows need to soften and absorb the movement to keep your hands steady in one place.
Although you have nice equitation on the horse it doesn't appear that you really have any effect on his way of going other than you get to choose the gait. You need to learn how to establish a forward rhythm and a contact and start riding your horses on the bit, forward and in self carriage. This takes a lot of miles with shorter reins and more focus. Keep riding and try to learn how to get the horses on the bit and working more over the back. This is learned by trial and error and developing a feel and can take years, so don't get discouraged!
Keep up the good work :)