Reading your response, a memory (from quite some time ago) resurfaced of a similar problem I had.

Given the length of time that's passed, I won't guarantee my recollection is perfect, but I seem to recall that I had an issue where perlbrew itself was invoking the system perl via the shebang line.

#!/usr/bin/perl
[download]

The perlbrew script is installed under the user's home directory. For me:

$ which perlbrew
/Users/ken/perl5/perlbrew/bin/perlbrew
[download]

I manually modified that. I believe I only changed the shebang line (and, thankfully, added comments about what I did). Given the executable part of the script is tiny, here it is in its entirety (minus POD):

#!/Users/ken/perl5/perlbrew/perls/perl-5.18.1t/bin/perl
# Use a known, stable perl version (with App::perlbrew installed) inst
+ead of:
##!/usr/bin/env perl
# which never has App::perlbrew installed when a new perlbrew perl is 
+installed
# or
##!/usr/bin/perl
# which is a system perl not to be modified (e.g. by installing App::p
+erlbrew)

use strict;
use App::perlbrew;

my $app = App::perlbrew->new(@ARGV);
$app->run();

__END__

... remainder of file is POD ...
[download]

I have installed, and successfully used, three more versions of Perl since perl-5.18.1t:

$ perlbrew list
  perl-5.14.2
  perl-5.14.2_WITH_THREADS
  perl-5.18.0t
  perl-5.18.1t
  perl-5.20.0t
  perl-5.20.2t
* perl-5.22.0t
[download]

So, at least to date, this tactic has worked well. Perhaps it will for you as well.

"... was to trash my system Perl."

I understand you did what you did for pragmatic reasons; however, I rather expect this will come back to bite you in the bum. My recommendation would be to reinstall the system perl; although, as I've never had to do this, I'm unable to advise how to go about it.