The media outrage on Twitter right now is pretty hilarious. I highly doubt it’d be the same if it was a 6-10 Carolina team getting screwed by an obvious tank job.
How about not going 6-10 and relying on help to make the playoffs in the first place?
I'm still p---ed that a 7-9 Pats team got hosed out of the playoffs 
I'm still annoyed that the 11-5 Pats team in 2008 got hosed out of the playoffs!
And I still say that having division winners automatically make the playoffs is a foolish idea. If an entire division stinks, all of its teams should just be left out of the playoffs.
It works the other way though as well. Why should a team like the Patriots get rewarded for 15 years by playing in one of the worst divisions in the sport, while a team like Steelers consistently played in a division with 2 other teams that made the playoffs the same year. Why have divisions at all? Why not just play a 15 game schedule and play ever team in the conference 1 time and don't play anyone from the other conference? That seems like the fairest way to do it. Everyone has an equal shot and the seeding is perfect. Then the Superbowl is full of even more intrigue since there is no intermixing of conferences.
I see your point, but the Pats were a legitimately good/great team in a weak division—as evidenced by their many Super Bowl appearances and wins—whereas this year's Washington team is, at best, a mediocre team in a weak division. I don't think anyone could make a valid argument that those Pats teams shouldn't have been in the playoffs, whereas this WFT squad ... very iffy.
I do like your idea of a 15-game schedule in which each team plays every conference opponent once each. And give every team a second bye week to maintain the current 17-week schedule while giving players more rest.
except New England had a disproportionate number of byes and home playoff games because the AFC East was so bad, so you have no real idea how good they actually were. They were 4-3 in road playoff games during the entire run, winning the 1st in the 1st year and the last one against the Chiefs three seasons ago. So during the majority of the run the Patriots were 2-3 on the road in the playoffs. They also had byes almost every single year. That advantage is immense season after season, and they got all those byes and home playoff games in a large part because the AFC East was downright terrible. So Brady has just 4 true road victories in the playoffs. As a comparison, Joe Flacco has 7, including 2 in New England (2009 and 2012). And take 2011, New England was 13-3, Baltimore was 12-4. So when they played in the conference championship, the game was in New England. That year Pittsburgh was also 12-4 and Cincinnati was 9-7, both made the playoffs (the AFC East had an 8-8 team and two 6-10 teams). New England only had to play 8-8 Denver before that game in the playoffs, while Baltimore had 10-6 Houston. You play that game in Baltimore and it probably has a different result. And that year, the Steelers beat the Patriots in the regular season, a team Baltimore beat twice during the regular season (Pitt's other 2 losses were on the road to 10-6 Houston and on the road against 13-3 San Fran). And that year the two divisions that the AFC East played had division winners at 8-8 (AFC West) and 9-7 (NFC East), while Baltimore was playing the AFC South (10-6 winner) and NFC West (13-3 winner).
So you can't have it both ways. You can't act like there isn't a benefit when a good team plays in a bad division, but then get made when a bad division has no good teams in it. You have to take the good with the bad and really recognize it for what it is.
