While the deck has less movement options than it would out of their base outfit, 108 Worldly Desires helps immensely by increasing your chances of winning lowball (or not cheating in lowball) giving you the important first action in shoot outs.
On shoot outs - if you suspect a 3x16 deck or a tighter draw structure, you rarely want to get into resolution. Your goal in these is to kidnappin', Legendary Holster, and then Make the Smart Choice home.
On Landslide - Kidnap, Kidnap, Kidnap. Although you start the game with 6 Inf, you don't have a ton of it sitting in your deck so your best option is going to be to try to get rid of their high INF dudes and camp every one of your guys on their deeds. They can't fight you so even Benjamin Washington and Xiaodan Li have serious kill pressure.
(but seriously, starting 6 Dudes and 9 GR on T1 is awesome.)