Straights aren't scary. You need to make entering shootouts scary, or opposing Shooter decks will walk all over you. I tried a deck very similar to yours when the base set came out after GenCon, and it did well in a few games until my opponents realized that a legal Full House would walk all over me.
Also, if you aren't running at least 2x Bounty Hunters at this point, there's no real reason to play Law Dogs. It's the only way to make their Outfit even remotely worthwhile.
My recommendation if you really want to stay with the "Non-Cheatin' Straight" theme would be to drop your draw structure to 9x of your A-thru-5 Straight draw values (in the deck, not your starters). That's 45 cards of your deck. Assume your starting 4 dudes don't count towards this total. Of those 9x on-value for each value you'll want 3-4 to be Clubs so they stay within your deck for consistency later in the game.
That gives you room for 7x off-value cards. At least 2 of these should be Bounty Hunters. The other 5 can be any of the cards I mentioned above (though Shotguns are on-value for you, along with both 4C War Paint and 5C Bad Company to go with them).
Straights aren't scary. You need to make entering shootouts scary, or opposing Shooter decks will walk all over you. I tried a deck very similar to yours when the base set came out after GenCon, and it did well in a few games until my opponents realized that a legal Full House would walk all over me.
Ways to make your shootouts scarier include: 3H Shotgun QH Legendary Holster QC Takin' Ya With Me KC Point Blank
Also, if you aren't running at least 2x Bounty Hunters at this point, there's no real reason to play Law Dogs. It's the only way to make their Outfit even remotely worthwhile.
My recommendation if you really want to stay with the "Non-Cheatin' Straight" theme would be to drop your draw structure to 9x of your A-thru-5 Straight draw values (in the deck, not your starters). That's 45 cards of your deck. Assume your starting 4 dudes don't count towards this total. Of those 9x on-value for each value you'll want 3-4 to be Clubs so they stay within your deck for consistency later in the game.
That gives you room for 7x off-value cards. At least 2 of these should be Bounty Hunters. The other 5 can be any of the cards I mentioned above (though Shotguns are on-value for you, along with both 4C War Paint and 5C Bad Company to go with them).