Hope I am not jumping in too late and that my suggestions have not already been covered by everyone above.
Though I've been riding many years, about half of them were spent without lessons after I stopped showing. As as result, my position went south. My point in telling you is that recently I started with a trainer again, and in many ways it's like starting fresh...so I feel your pain! Some of the reminders I've gotten in lessons have made a huge difference in how Playday (the 4yr old OTT Standardbred I lease) responds, and have helped to put me on the path of being a more effective rider.
When at the trot in your video, it appears that you're 'archy'. Meaning....sticking your toosh and chest out while arching your lower back. By tucking your toosh (think riding on your back pockets) it helps your horse tuck too - plus it's easier on his back. One really helpful visualization (for me, anyway) is to think about the horses's back mirroring yours. If you're archy, so is he! You want him/her reaching under, using their hind end, relaxed. Keeping your own lower back/abdomen relaxed and not pushing backward will help! The other thing I noticed was your posting position. Instead of using your quads to post, (resulting in a more thrusty motion) think about letting Paradise's movement gently propel you out of the saddle. It should be a lower up and down movement instead of hips pushing forward diagonally out of the saddle. Focus on using the muscles on the back and inner leg instead of your quads. Someone mentioned riding without stirrups - this is a great exercise to discover and learn to use those muscles! Another is to post side to side, which helps you loosen up though the hips and find your center better. To do this, start posting in the same rhythm you would if riding normally, then begin getting your right seat bone going across the saddle into the left and vice versa - but don't do way up out of the saddle and over...just over. Another loosening up/finding balance/not using the quads exercise is to post the trot going down down up instead up down up down. This will help you loosen up and relax, practice tucking your tail and find those posting muscles!
I hope the above ideas help you as they've helped me! One other suggestion - don't try to fix everything (ands, feet, leg, back, etc) all at once. Think about improving your position like lifting weights...it's about focusing on one muscle at a time and slowly building strength, until one day you find you can do a ton of reps at a high weight!
That said, I too appreciate your openness to suggestion. When being critiqued in a lesson or otherwise, it can feel as though you are a hot mess! But the truth is, no-one is perfect. We ALL have a lot to learn and improve on, and you and your horse (I can tell Paradise wants to do well for you! To my eye, he is willing, just confused about what you are telling him) do make a nice team which will only get better with practice! Which - once you've moved and get lessons, will be by leaps and bounds :)