There is also the option of dropping "he verbed" entirely.

This can cause problems. Sometimes when I read a lengthy dialogue in this style, I read a line which seems to me much less likely to by said by character whose turn it is to speak, and I have to go back to the last anchor point where it was made explicit who was talking, and carefully keep track of it. In some cases, after doing this, I have wondered if the author lost track.

Being clearly understood is more important that avoiding the appearance of redundancy.