Dude, you missed the most important object in the room. There is a box on the table, across from where you picked up the cash. It contains Schofield Revolver, one of the best revolvers in the game. You can start this mission, by just going and have a look through the back window. You don't need to find the lady who gave you the information. Just get the cash, and Schofield Revolver off the table, and leave immediately. You can hitch your horse right in front of the Sheri's office, for when you are making your escape. If you move fast, no one would be any wiser and you can make your escape easy. Can do this in any stage of the game.The best time is when you start the Chapter 2.
I hitched my horse next to the doctor’s office at the sheriff’s hitching post, then went in and robbed the Register, pile of cash, grabbed the schofield, looted the 4 bodies, blew open the safe, knocked out the one sheriff who came in by that point then ran outside and hopped on my horse and blazed a trail outta town. Only ended up with $13.00 bounty. Not too shabby. What’s the full the take again ? Whatever it was, it was def worth it. Unfortunately there’s no way to rob the doc without alerting the law since the sheriff is next door. I’ve tried both throwing knives and arrows with no shots fired by anyone and still get the alert signal.