So, this is a quick rejiggering of BlueonBlue's 2015 One Base Set Law Dogs deck: https://dtdb.co/en/decklist/408/one-base-set-law-dogs#. I can't promise my additions made it better, but I felt that tightening up value structure was important.
This deck is intended as a pair to a 108 deck out of, each built sharing a total of x1 Base Set, x1 Immovable Force, Unstoppable Object. This limited card pool necessitates certain compromises... though I feel this Law Dogs deck is still pretty solid. (I think its main limitations come from only having x1 Core, rather than having to split that Core with another deck.)
In that case, it would be a reasonable play, I think, to start Andreas Andregg in place of Ramiro, as this would leave you with a guaranteed 5 GR after lowball even if you lose (and thus leave you able to afford any deed you draw). Esp. if Hamshanks is in the deck, so you don't start with 1/2 your Spade 5's in play. It would also leave you with 1 more influence; 3 inf. is a very low start. After 1 fight, Andreas only costs 1 more than Ramiro... .
Alternatively, Wendy is a powerhouse. You'd gamble on being able to afford a 5-cost deed T1, but Travis can help you cycle for a better opening hand, and if you win lowball everything would be comin' up roses. :)
x2 Charlie's Place is almost certainly better than x2 Pearly's Palace... but this deck can afford the latter (and can camp Clementine Lepp there from T1). Pearlies is also a piece of anti-Shotgun, anti-Holster tech... and it seemed brutally unfair to put Pearlies into the other half of this matched pair! (Consider running x2 of each in a non-paired build...).