How do you transition solidly to the Shuto Uke in the Heian Shodan kata?

A good question. One that is also hard to explain without demonstrating in person. In some versions of the Kata it is correct to end up in a Neko-Dachi. The transition of the turn can be improved by doing the turn into the correct stance by doing it very slowly until you have it corrected. Over the years I have noticed that if a student makes a step incorrectly, then moves one of their feet to fix the stance, they never learn to make the transition to the correct stance. They simply keep correcting the foot position after it has been done wrong. To fix this problem the student MUST do the turn/step/slide... etc correcting the transition as it happens, not after it has occurred. An example of this is a student that makes a 90 degree turn to their left. Many end up to narrow, because they did not place their left foot where it should be. To make matters worse, they try to fix the problem by moving their right foot out wider. This will never teach them to put their left foot where it should have been. Only by doing it slowly and correctly can they overcome the bad habit.

Now you don't indicate if you are having trouble with the transition of your hands in this situation too? If you are then I can offer this. In the first version of the Heian Kata, we were taught to circle the hands to enter the Shuto. As I turn from the last punch, I drop my left hand to my center and roll it in, up and over. At the same time my right hand is also making the same circle, but exactly at the other side of the circle the hands are making(180 degrees opposed to each other).

Hope that helps.....

OH Yes, we don't see the shuto as being a block. The first hand that ends up being closer to your body can be deflecting a punch to the side, while the shuto is a strike to points on the attackers neck.

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There is a principle called consolidating your balance in TMA and in that lies your answer. Bring that back foot up, consolidating your balance under neath you and over both feet and then extend it back out to that first back corner resting the ball of the foot on the floor, toes curled up slightly. Then pivot into your stance as you are doing this as your foot reaches the proper distance for your kokutsu dachi setting up your shuto and executing it as you make that pivot into it.

For training purposes I have my students place their hands on their hips sometimes and practice doing their katas from the waist down only, doing all the stances, turns, pivots, etc. This allows them to work on those aspects a little more fully and focus on how well they are doing only those aspects of the kata and develop them to a finer edge and level of execution. You may want to incorporate that into your training and when you practice your katas and I bet your instructor will notice a difference in a few months on how well you do your kata.

I am totally unfamiliar with your Kata. I do no this from years experience teaching TKD. If a student feels unbalanced it is 99.99% of the time their stances are off. I have them do what someone already suggested and I will repeat it for emphasis. Do you entire kata with your hands behind Your back or tucked in at your sides. Focus on your stances and the transition from stance to stance. We do drills I call "stomp stomps" and "step slides" which are just transitions from stance to stance. I find this helps some of the students focus on footwork. When the foot work is good everything else gets easier and seems to flow better. Too often we forget to check our footwork focusing to much on the blocking and striking forgeting that without proper rooting everything loses power.

I must agree with pugspaw on this. After learning and teaching and learning even more as I began to teach it is proper foot placement that is the problem for many student especially in the beginning. I spend quite a bit a time teaching footwork, foot placement and how to turn. If yo don't have those you will never have the correct posture, balance or power to execute techniques.

lots of good advice here, difficult to add, i like pugpaw answer as well as the others..

i would add you want top move from your center maintain your balance. foot work is import in keeping balance as well as moving from the hips, and going through transitional stance before the backstance