After some more time with the issue, the issue is when the agenda has items A, and next line, invisibily (due to org-agenda-dim-blocked-tasks), B.  Trying to set A gets you into an invisible loop because moving to the start of the line after displaying the time in org-agenda-show-new-time doesn't take you far enough back to proceed backwards.  The next iteration through the loop, the time will be re-displayed.  

Removing the (beginning-of-line 1) at the end of the time display code in that function, and substituting (org-agenda-previous-line) seems to fix it.  I'm not sure if that's the right approach - the previous code didn't use that function for a reason, but I don't know what that reason was.