In all honesty we cannot win. If the final 7 I would say the order of most likely to least likely to win if in the final 3 goes
Bears have historic love with the 85' team and haven't been good in a long time so few will hate them
Packers also have historic love and are actually one of the teams that a lot of people like them even if they aren't fans
Patriots have the "fuck the ELoE" vote which is growing stronger every day
Niners haven't been relevant and don't have a lot of love outside their fan base but they are a historic team with Rice and Montana who can land them some votes
Giants beat the Pats twice and aren't as hated as some of the other NFC East teams but the fact that they have the NFCE voting against them makes it hard
Steelers are a historic team but there is little love for them outside of their fan base. They have some likable players but no Polomalu who can really rally the voters. Little chance for them to win
Cowboys are just too hated and don't have enough going for the them. The NFCE will never vote for them and they have rivalries with many of the other big teams. The only saving grace is Romo retiring and Dak and Zeke but it is highly unlikely they make it.
I think the best bet for the Cowboys would be to go into the finals with the Packers and Steelers. The Patriots are guaranteed to win if we go in with them and the Packers as their will be too many "fuck you" voters as well as some people mistakingly voting for the Patriots to win as the format is different in the final round. If we go in with the Bears or Niners the pitty votes will win out and if we go in to the final 3 with he Giants the third team is a lock to win as the NFCE would all go to the third and we wouldn't have enough support outside of it.
Going in with the Packers and Steelers gives us the best chance but it would still be very unlikely. We'd basically have to hope the Pats vote for us to stand a chance. Eagles vote Packers and Seahawks vote Steelers but there's enough bad blood from teams all around that the Cowboys have a chance. Over the past decade we have been the least successful of those 3 teams and hopefully won't have as much hate against us.
So there's my entirely too long analysis of this pointless game. Basically the Bears, Giants and Niners need to go followed by the Pats if we have any chance st all.