They have a sit and stand stroller that is also a double stroller. We just borrowed a sit and stand to go to Disneyland and it was absolutely wonderful! I am going to go buy one myself. We did not give our son a choice about sitting or standing on the back platform. He loved the freedom of being able to chose between sitting or standing. He was only allowed off when we got to each ride.
I found the traditional double strollers hard to push with my 35 lb four year old in it. I have used a Graco, Safety First and Eddie Bauer double stroller and all three were the same. With him in the back of the sit and stand it distributed the weight more equally between the two kids. When he wanted to nap we just had a blanket that he could lay his head on against the handles in the back or we put him in the front.
Well, I hope this helps. I know you said you didn't think a sit and stand would work, but with a four year old this might be your best option. I am going to look into the sit and stand that is the double stroller with the back platform as well, so when we have our third we can all ride comfortably. Good luck in your search.