Just alternate idea, please, excuse my typos, I write it directly to browser form.

Concerning just

use lib 'modules';
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, you can have

package Base::MainApp;
use Base::FooBar;
sub new {
  my ($class, $prototype) = @_;
  unless (ref $prototype eq 'HASH') {
    $prototype = {foobar=>Base::FooBar->new()};
  }
  my $self = bless $prototype, $class;
  return $self;
}
sub method_using_foobar {
  my ($self) = @_;
  $$self{foobar}->foobarize();
}
#rest of module
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and

package Client1::MainApp;
use base 'Base::MainApp';
use Client1::FooBar;
sub new {
  my ($class, $prototype) = @_;
  unless (ref $prototype eq 'HASH') {
    $prototype = {foobar=>Client1::FooBar->new()};
  }
  my $self = Base::MainApp::new($class,$prototype);
  return $self;
}
#rest of module
[download]

But it very depends how the current code is organized...