I think you should be able to adapt this to your needs by rewriting the package Bogus as follows:

package Bogus;
use strict;
use X11::GUITest qw(SendKeys); # and whatever other functions
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(and maybe also renaming it away from Bogus to, say, Class::X11::GUITest), and then using that from the package MyBogus:

package MyBogus;
use Moose;
use MooseX::NonMoose;
extends 'Bogus';

around ...;
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In theory, you should even be able to do away with the intermediate Class::X11::GUITest class by using the following:

package X11::GUITest::Moosified;
use Moose;
use MooseX::NonMoose;
extends 'X11::GUITest';

around ['SendKeys'] => sub {
    ...
};
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