Tom, you obviously love your son a lot and that is most important here. I can understand that the lack of a parental 'side-kick' (no pun intended) can be stressful.
I am sure that since you both have the love for baseball you play catch with him a lot! Why not put on a pair of old jeans and after he seems to slack off on the passes in baseball, get on your knees and fight him. Let him have that Dad -n- son time and just the pure fun of it! Show him an easy move and let him practice it on you and he will want dearly to go back to 'karate class' and show it off.
I believe the tie-in you have made with Uechi and baseball is a good one! So very very WELL done there! Depending on his age, Uechi may not be his thing right now. I started when I was 8 and after I got my 8th jyu, I just was not interested anymore. After about 2 years of a "Break" I came back to it and have loved it since. At the time, my Dad, Mom, brother, and sister were taking it and one by one , we all lost interest and the PUSH from the others was not there. Also, my Dad could not have told me anything at the time that would have made me go back to class. I simply did not enjoy it anymore and was not going to have fun or do it anymore. Now, in the last years, I have helped teach the little kids and have gond to every class 5 days a week (helping and/or learning) except for about 12 classes that I have missed! That says a lot I think. Now I enjoy it and I think having that break and my OWN will to start back gave me an option. I know you are not forcing him to do it, but you simply realize after the two-weeks of wanting to quit, he will love it for 2 months. And getting over that hill is the hard part because you know he wants to continue once he gets over it. I think you are doing a good job and looking towards other karate-ka is a good place to find answers. I have tried and maybe soem of this will be useful. Good luck