I know this is not what you want to year since you're giving up faith on him, but I would go with Walter, simply because he has the most upside out of any of those WRs.
As you said, Avery is brittle and has done NOTHING all year. The lions are also pretty weak against the run so I expect a heavy dose of SJax all day, as that seems to be the only way the Rams can move the ball on offense. As for Braylon, he has shown nothing since his amazing first game with the Jets, and with the regression of Sanchez, return of Cotchery, and the success of the running game, you have to think he isn't gonna get a lot of targets.
That leaves Walter, who despite being a disappointment, is still a starting WR on an explosive offense who happen to be playing a below average defense. He should get the start over the other two.