There was a thread where we discussed Caesars Tumor a few months back. Bascially, you can't do what you want to do.
Now, for the Goodsprings Gunfight. Here is what I do. I skip the whole thing with Ringo when I am in Goodsprings and then leave once I am done with the other parts of the Tutorial. I don't even go into the Saloon again to talk to Trudy when asked.
Now, as to how to handle the fight. Once you are ready, and I am once I am done with Primm, but this can be at any time, I go and talk to Trudy and set those events in motion. I can sneak snipe the PG Leader while I am gathering resources as he just stands by a building in Goodsprings and get no impact as long as I am sneaking. He has the most hit points and the strongest weapons and armor. The rest are canon fodder.
Here is where it gets tricky. I mine the road and the sides of the road that the PG gang will walk up during the fight. At higher levels, it takes a bunch of these as I swear the gang is invincible at the very beginning (100 satchel charges and 25 C-4 did not kill them). So, spread them around and set up 3 areas as they will not die on the first blast no matter what. Then I go see Ringo after getting help from the town. I go into Sneak mode before I leave the Gas Station and let the mines do their thing. I sometimes snipe the PG from the gas station while hidden, but I am usually in Caution so I get a PG Faction Loss if I do that. Most of the time, the Goodsprings folks can finish off the PG without losing anyone if the mines have weakened the gang. If you let the Goodsprings people completely take care of the fight, including not mining the road, then you suffer no loss in PG Rep. With the Mines, you might get Shunned as they recognize them as yours (one time I was not dinged, the other 4 times I was). Note, make a save before you leave the Gas Station, as I was at Hated a couple of times doing this with Mines.
Now, if you handle the quest at Vault 19 the right way, you can gain back PG Rep to the level of Mixed if you get Shunned in Goodsprings.