I have switched my visa status from H-1 to J-1, which is valid from Feburary. An H-1 holder is allowed to stay in the US for up to 6 years and I consumed it at the end of January. To stay longer in the US, I decided to apply for a J-1 status,which allows you to stay in the US for 5 years.
It is not uncommon to switch from J-1 to H-1 but it seems much less common the other way around. But I didn't have any problem getting a J-1 visa. You could transfer your status from H-1 to J-1 while in the US. However, I was told that it would be more complicated and take a longer time than applying for J-1 afresh in Japan, which I did. I got a J-1 visa in a week.
When entering the US, I presented my J-1 visa stamp and DS-2019 and got I-94 with D/S (Duration of Status).