Turns out that Put_() has an UNDERSCORE even though the Win32::OLE docs (vaguely) give this as merely "Put()" -- use the underscore and it works.

my ($init, $max) = (256, 301);
for (in($PageFiles)) {
  showProperties($_);
     $_->{InitialSize} = $init;
     $_->{MaximumSize} = $max;
    $_->LetProperty('InitialSize', $init);
    $_->LetProperty('MaximumSize', $max);
    $_->SetProperty(InitialSize => $init);
    $_->SetProperty(MaximumSize => $max);
    $_->Put_()   # with UNDERSCORE in method name
      and print "3 Put_: "     . Win32::OLE->LastError . "\n\n";
  last;  # just change 1st one
}
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Another thread here indicated the "Exec Query" SQL like interface is READ ONLY and offered the getting "instances

#my $PageFiles = $wmiService->ExecQuery("Select * from Win32_PageFileS
+etting");
my $PageFiles = $wmiService->InstancesOf("Win32_PageFileSetting");
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But that had nothing to do with my problem -- both methods work as long as you use the proper Put_ (with underscore) method. All 3 setting methods (hash assign, Let, and Set) seem to work fine even though not sure the differences if any.