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Beyond the Beef - Mortimer
In order to start the quest, even if you plan to help the cannibals, you will probably need to talk to Heck Gunderson. He's at the bar inside the Ultra-Luxe Casino. He has a hired guard with him, so he's easy to spot. He'll explain that his son, Ted, is missing and ask that you see what you can do to find him.
To do the quest officially, talk to Majorie first. She's in the Gourman at the reception desk, usually. Talk to her, but don't mention that you're a cannibal or use the Speech check. She'll just be disgusted and you'll gain infamy with the White Gloves for no reason.
Talk to Mortimer next about the missing man. If you want to help him, you'll either need 62 points in Speech (odd skill check numbers in this quest by the way) or the Cannibal perk. He'll open up to you about his plan and ask that you help him convince the White Gloves to go back to cannibalism.
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Beyond the Beef - Handling Ted Gunderson
If you want to get a human for Mortimer's meal, you will have to pick one of three options.
If you don't want to use Ted Gunderson, you will need to free him and convince him that it wasn't actually the White Glove Society behind the kidnapping. If you have Mortimer's permission and key, you can just go to the Gourmand and use the marked door to go to the kitchen. Go down and walk past the guys with the flamethrowers. There's one guard down here, but you can use your legitimate excuse if he stops you. Just go into the freezer area of the kitchen and use the terminal to open the freezer door. Talk to Ted inside. If you have 38 points in Speech, you can convince him that it's just a false flag attack by his father's enemies. Led him out safely and lie to Heck Gunderson about the attackers.
Note - There's not much of a benefit to freeing Gunderson and going for the other source. While you can earn money from Heck, you can get twice as much by completing Pheeble Will and framing Heck.
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Beyond the Beef - Killing Ted Gunderson
For this one, you can just go down to the freezer as before, but you will need to kill Ted Gunderson. Note that you will have to either use your fists or holdout weapons. You might be able to get a shotgun from Heck by telling him that you plan to rescue Ted.
Ted's not exactly tough though, so you should be able to kill him easily with a silenced pistol or even just your fists if you can keep him pinned in the freezer or another room. Once he's dead, loot his body to get a jar of his blood. You'll need this to frame Heck Gunderson.
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Beyond the Beef - Framing Heck Gunderson
Go back up and walk over to the elevators and find the one that goes to the Penthouse floor. You're officially trespassing, so do it while you're partially hidden. It shouldn't be hard to get out of everyone's line of sight. Once you're in the penthouse, you'll either need as stealth boy or a decent weapon. Heck has two guards that are fairly well positioned. You can just kill them. If you have decent armor, then their shotguns will barely scratch you. I know that wearing Van Graff armor let me just punch them repeatedly until they died.
Regardless of whether you want to use stealth or not, get past the guards and go up to the marked bed in the corner. You should be able to use a context key to spread Ted's blood around it. Walk over to the sink that's a short distance away to leave some more blood.
Run back outside and talk to any of the securitrons on the strip. There should be one right by the gate to the next section of the strip. Report the suspected struggle to them to set the pieces in motion. After a brief amount of time passes, you can go into the Ultra-Luxe and find the securitron attemption to arrest Heck Gunderson. He'll pull a shotgun on the securitron and he will be killed. This counts for Pheeble Will and takes care of the White Gloves' problem. You can now safely just use Ted for the meal.
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Beyond the Beef - Alternative Meat Options
If you are willing to sacrifice a companion, you can just take them down to the Freezer and lock them in to secure the meal. Obviously you need to empty their inventory before doing this and you will need to have asked Mortimer about this option when he first talked about substitutes.
You can recapture their first choice, Carlyle St. Clair, by going to his house. It's just to the north of Freeside. There are a ton of ways to get him to cooperate. An almost ridiculous amount of choices.
There are two Speech checks to get him to go to the Ultra-Luxe himself. If you learn about his checkered family history, you can convince him to go with just a 45 Speech point check.
Black Widows and Confirmed Bachelors can trick him into going into the dumpster for a trist. There's a chain involving 7 points in strength and 45 points in Medicine and Unarmed that lets you knock him quietly. People with 45 points in Guns can just pistol whip him. If all else fails, just use the cattle prod to knock him out and drag him to the dumpster with the "Z" key.
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Beyond the Beef - Conclusion
To wrap things up, after you've prepared the meat you can talk to Mortimer to put the final touches in place. He'll explain the rest of his plan, which actually doesn't require you at all. At the next 7 PM, he'll host a big dinner in the members only room for the White Glove Society. You don't actually have to be there, and there isn't much of a real benefit. He sums it up and it's fairly simple. He lets them eat the meal and then explains that they've all already committed the offense, so they might as well reconsider their rules against it.
Once he has the dinner, you can talk to him and confirm that they are cannibals again. You should get your reward and a lot of reputation. This concludes the evil side of the quest. Remember to get your reward for "Pheeble Will" too.