My advice is no strict 'refs'; ## no critic. strict and perlcritic are meant to be tools that help you. When they are not helping you, you should disable them (in the smallest scope possible); you shouldn't be forced to jump through hoops.

That said, a bit of stash exploration can get you there...

use 5.010;
use strict;
use warnings;

{
    package Foo::Bar;
    our @ISA = qw(Quux);
}

sub get_isa
{
    my $klass = shift;
    my $stash = \%::;
    for my $part (split '::', $klass)
    {
        $stash = \%{ *{ $stash->{$part . '::'} } };
    }
    $stash->{ISA};
}

my $isa = get_isa('Foo::Bar');
say "Foo::Bar isa $_" for @$isa;
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That's actually less grokkable than using symbolic references.

There is a package called Package::Stash (used extensively by Moose) which wraps some of this up in a cleaner API. But my vote is to use symbolic references.