Okay. I bought Parallels — was previously running the trial version — and asked this question of the Parallels tech support team. Here is their reply:
You can access your Mac files from the Network drive. Click on the Parallels shared folders on the Windows Desktop. In that folder you will find Home.psf and Host.psf. You can access the files from Home.psf and Host.psf folders.
So my error was in assuming that I could access the internal Mac drive in Parallels as "Local Disk E," as in Boot Camp.
From within Win 7 applications running in Parallels, once I located "Home on 'psf' (Z)" at the very bottom of the list of volumes, I was good to go. All files on my Mac drive were accessible.
And it worksgreat!