Your aikido friend gives sage advice.
I am want to say that anything you do in martial arts takes at least a thousand repetitions before you get it down.
There's a lot of good advice given here. But I'd like to add to it.
We've had many, many wars on the Fora over prearranged (yakusoku) kumite like Kyu, Dan, the Kenyukai exercise, the Shohei Ryu exercise, etc. A lot of the criticism come from folks not understanding the purpose of the exercise.
Prearranged kumite are designed to help you get your feet wet with a partner in a very controlled environment. If you spend all your time thinking that the goal is to teach you self-defense applications, we'll you've completely missed the point. It isn't the what, but the how. And you need to take this exploration into the how and run with it.
Dana captured the idea of the art of ukemi (a.k.a. rolls and falls). The idea is that it's an exercise which teaches you how to get hit with high speed dirt. But it's just a different kind of kotekitae (forearm conditioning), ashikitae (leg conditioning) and karadakitae (body conditioning). I believe that so strongly that ukemi is part of the requirement in my dojo in the kotekitae part of the test.
Fred and Van are right about going elsewhere to get training on ukemi if it's not a regular part of your dojo training. In my opinion, this is one of the biggest holes in Uechi Ryu. We have a style that allows for grabbing, grappling, and throwing, and yet the Okinawans taught us to treat it like a striking style. Why? Because that's what contemporary Okinawans taught in their dojo businesses. But the truth is, Uechi as a striking style is lacking when you take in the full depth of what both Kanbun's art and Okinawan martial arts in general can be.
Why did the Okinawnas short-change us? Because they don't do what the jujutsu, judo, and aikido people do - teach ukemi. If you don't do ukemi, then you won't have students to train with in grappling in much the same way as you won't be doing partner work and sparring (sans equipment) if you don't condition the extremities.
So if ukemi isn't a REGULAR part of your training in your Uechi dojo, then go elsewhere and pick it up. Once you do so, then this simple fall in Dan Kumite will be a piece of cake.
I have ukemi as a requirement (along with kotekitae) on the very first belt test. And while we train on mats (to prevent people from developing bad habits that can hurt them), I make students do most or all of their ukemi on a test on a bare floor. Why? If you're afraid to roll and/or fall on a smooth floor without glass, gravel, and other stuff, you are toast on the street. But if you don't fear the floor, then you won't fear the grappler.
You can and you will get better at this. When I started, my teacher (who started in judo) used to nickname me "The Albatross" because of my ungraceful landings. I even did that grab-the-sidekick-spin thing a la Matrix one time in front of my teacher's dad, and goofed. (I spun the wrong way, and ended up separating my shoulder in front of his dad.) But I put in my time. Over time (as your friend suggested), I learned how to contort my body (sort of like Jim Carrey with his plastic face) and found out that it was possible to round all my edges. That's pretty good considering I'm built like a crane. Then I learned how to teach it to others.
If The Albatross can become a good ukemi instructor, then you can do it as well.
Next thing you know, you'll be seeing and practicing things in your Uechi style (with good partners) that others only dream about.
Come to camp some time and work with us. Joey Pomfret (Uechi/BJJ expert and former MMA competitor) is a great example of a guy who can put it all together. But there will be folks there (including yours truly) who will be happy to help you learn how to make the earth your friend.