The project that triggered a heap error has now finalized/exported. The version of the file that failed earlier now works, so the problem was not the project file.
The reason is apparently what I suspected - too many projects being read into my iMovie used up too much memory.
I moved all completed projects out of the iMovie Projects folders into differently named folders.
Being 32 bit might be complicating the issue, but the real solution is to not have unneeded projects for iMovie to read.
One would have thought that Apple might have discovered this and "warned" users.