Thus far, I have (just...) attempted the following:

1. Reasoning that ExtUtils::MakeMaker was probably “the” key module that needed to be brought up-to-date, I removed files from the previous attempts and tried install ExtUtils::MakeMaker.   The command seemed to succeed, but it generates a peculiar message, all skipped: ExtUtils::CBuilder not installed or couldn't find a compiler.
2. Attempting to install ExtUtils::CBuilder complains that ExtUtils::MakeMaker version 6.31 required--this is only version 6.30   And so it is.   The installed-version of this module (which I had attempted to update in step #1) is still 6.30 whereas the current CPAN version is 6.56.

Looking at the logs, I see that CPAN indeed did retrieve what it thought was the correct version:
ftp://cpan.netnitco.net/pub/mirrors/CPAN/authors/id/M/MS/MSCHWERN/ExtUtils-MakeMaker-6.56.tar.gz

Well... when I use the command i ExtUtils::MakeMaker within CPAN, I can plainly see my problem:

DESCRIPTION Writes Makefiles for extensions
CPAN_USERID MSCHWERN (Michael G Schwern <mschwern@cpan.org>)
CPAN_VERSION 6.56
CPAN_FILE M/MS/MSCHWERN/ExtUtils-MakeMaker-6.56.tar.gz
DSLI_STATUS SupO (standard,comp.lang.perl.*,perl,object-oriented)
MANPAGE ExtUtils::MakeMaker - Create a module Makefile
INST_FILE /usr/lib/perl5/5.8.8/ExtUtils/MakeMaker.pm
INST_VERSION 6.30

That is not the place where I thought ...

(Blink.)   “Oh, damn...”

Effin’ PERL5LIB ... yup, that was it.   Well, I guess I’m not gonna delete this, but ... boy, do I feel stoopid.