
As it's not specified that you have to draw it from your deck, you can use Katja Eastbank to "store" the 3 copies of Quick Shot and then use her action to draw them during your turn. This way, for 1 action (her ability), you play Quick shot for free (the trigerred ability).
Of course, if you are engaged with the enemy you take an attack of opportunity, but it's in a Tommy Muldoon deck so you should be able to handle it and it works without AoO against Aloof enemies or enemies engaged with other investigators.
More costly than OrionAnderson's combo with Hunting Jacket (resource- and action-wise), but with the added benefit that you replace the - then useless - draw of Quick Shot by the draw of an other card.