You should post this in the Tech or the Toyota forum. While I have not had experience with this directly on the NZE Corolla, this is a common occurence on BJ 323s. The hard start may be caused by a number of issues, so get a good mechanic to check it out, before spending money wildly.
I suggest you try the gents at State of the Art Automotive.
viewtopic.php?f=6&t=355894