I tried your bowling in my room lol. It i hard to bowl like that for me now. I used to bow kinda like this in highschool as a leggie. As years went on (21 now) I learned that orthodox leggie was better for me as i naturally had a double jointed shoulder and rubbery wrist

. This meant I can turn about a metre if i wanted to , my dip were also intense making my Topspin brutal. Working on slider, flipper and accuracy. If you can bowl like how you are bowling now you can bowl leg spin. You are going to have to bowl quicker, with more flight and need subtle several small variations at least.
I kinda was doing what you were doing, bowling leggie kinda like yours with leg spinners bowling action, no side on action nor i had a proper run up. I was getting yelled by my club team mates who were in late 20s and early 30s for not having a run up, side on action and etc. Then i read the book
THE ART OF WRIST SPIN BOWLING by Peter Philpott. Ordered it online and within a month learned a lot. I suggest you read it. You will love it. The book was written in early 90s when Warnie was kinda new and the contents are from 60s,70s and 80s. Don't worry they can still be applied today.He coached SL in 80s and complains how SL cricket don't give priorities to spin bowling and suggested that Sri Lankans had the best physique for spin bowling, look what happened 30 years later with Murali, Herath, Mendis and other spinners coming up. I learned how things like run up and side on action help you go long way in cricket. He also teaches you how you can bowl leg break in 3 different ways. He teaches you how to get maximum drift, maximum dip, and mixture of both. It will help you big time, you are a leggie in denial lol. My suggestion to you is, get a proper run up, you will eventually get yours, don't worry if you can't get it in a week, you will end up with one and make sure your run up isn't part time spinner's running,stopping and throwing. Side on action is important, it helps you transfer power from your back leg to front leg which helps your bowling speed along with your non-bowling elbow. Side on action helped me bowl faster. Im still skinny-fat with belly and scrawny legs, i need to work on strengthening my legs because I still need to bowl 10-15km/h faster than now.
Every spinner starts of with bowling full tosses and short balls lol. It is normal, you just have to practice, practice and keep practicing till you get it. Side on action helps you more and you need side on action anyway. This is coming from someone who didn't bowl differently from you a year ago. You have flight and you can't bowl flat which is perfect for a good spinner. Good spinners don't bowl flat. Flat bowling won't give you wickets, flight bowling will. Slider and Flipper will be your only flat bowling. You can't bowl in matches unless you are developed, which is the negative side but once you have a good stock ball, googly and a topspin, you can start bowling in matches and work on your sliders and flippers. Order the book and give it a shot.