Made it to 1650!
Regarding the team...
Honestly, Alomomola is effective enough as a physical wall that I'm considering upping her defensive investment and changing Skarmory out for something else. Because Defog is so vital for the team thanks to Shedinja, I find myself reticent to bring Skarmory out recklessly. It doesn't help that I'm pretty much forced to run Shed Shell to keep her from getting trapped, which in turn means I don't have any passive recovery and often have to choose between Roosting to keep Skarm alive or doing something useful. I end up leaning heavily on Momo as my defensive wall.
Of course, if I do that, I'd probably need to up Momo's defensive investment, which would make her less useful overall. Right now I've got a mixed spread defensively, so that she can counter Keldeo, and the standard defensive spread has a chance of getting 2HKO'd by Specs Keldeo's Hydro Pump. Instead I'm currently running 56/252+/200, which is enough to avoid the 2HKO from anything Keldeo can throw at me even with rocks down and helps against stuff like Megagross Grass Knot. I had originally been using Knock Off, but I've switched to Toxic so I can threaten CharX, who is a serious pain if it has both EQ and a Fire move (CharX lacking EQ loses to Heatran, CharX lacking a fire move loses to Sheddy).
Shedinja is Shedinja. While it's not a gamechanger every battle, just having it on my roster is an advantage. Seeing it there pressures most teams to try to get hazards down at all costs, which puts the game on my terms, since my team is all about hazard control. It's also such an absolute counter to what is arguably the biggest threat in OU, Megagross, that it's worth its weight in gold just for that alone. Oh, and it steals free ladder points off of BP teams, which is a gas. Now that Espeon pretty much has to run Dazzling Gleam to beat Sableye, it doesn't have room for HP Fire or Shadow Ball, so Shedinja just laughs at it. It's also just fantastic against rain teams, who rarely have more than two or three mons that can even touch it (Ferrothorn is hard countered by Sableye, so they're down to Kabutops, who is easily stalled out of Stone Edges and super predictable, and maybe Torn-T or Toxic on Politoed or something). It's also a great defensive pivot in general, since you pretty much always know what's coming after you switch it in. Bring it on on a Thundurus, for instance, and you know that they'll either Knock Off, HP Flying or switch out. That gives you an easy switch in and reveals their set. Bring it in on something that occasionally carries Toxic or WoW, then pivot out to MSableye, and either they have switched out (if they lack status) or gotten their status bounced back to them. Focus Sash lets me be a little reckless, but I try not to reveal Focus Sash until it means doing something dramatic like surviving an HP Fire from Latios to kill with X-Scissor and deprive them of their Defogger.
The main three things to stop Shedinja from playing recklessly are Ferrothorn, Garchomp and Tyranitar. Ferro and Garchomp are fairly easy - just always click WoW instead of attacking, so that you don't die to Iron Barbs/Rough Skin damage if they try to surprise you and switch them in. Once burned Garchomp is easily beaten by Sableye, and Ferrothorn can't scratch Sableye even without a burn. Tyranitar is a bit more annoying, but it really just means a lot of double-switching. You'll eventually wear it down with hazards and status, and then Shedinja is free to roam. Alternately, if you don't need it to specifically check something like Megagross or Manaphy, you can catch Tyranitar with a burn or X-Scissor on the switch and take him out of the game early.
The rest of the team is bog-standard stall core, Skarm/Tran/Mega-Eye/Chansey. The only real difference is that I run a lot of Protect, because it helps in scouting the opposing team's moves and also lets me do stuff like catch choice-locked Volt Switches or U-turns to block with Shedinja and give me a free burn or hit on the incoming manual switch.
The team has a couple of problems. More than half of my losses were due to either CM Mega-Sableye or stallbreaker Gliscor (especially the Taunt + SD version), both of which just run through this team without much I can do about it. I've seriously considered dropping Seismic Toss on Chansey for Skill Swap just to beat those two. Also, if I play too recklessly with Mega-Sableye early and lose him, that really kills my momentum for the game. It's possible to recover from it, but it's not easy. Bulk Up + Taunt Talonflame is also annoying, although it's relatively rare. All other versions of Talonflame are reliably handled by Alomomola plus either Heatran or Sableye. The only time I've faced it I managed to beat it, but only because I won what amounted to a 50/50. (He was in KO range from Seismic Toss against Chansey, couldn't KO with BB, and had to either Taunt or Roost. He guessed I would go for the Toss and picked Roost, but I went for the Toxic, which is the only reason I won.)
TL;DR version: Sheddy + Mega-Sableye = Fun Times. I'm probably going to keep tinkering with the team, but without a doubt I'd say that this at least demonstrates that Sheddy is viable in OU, although it requires a lot of careful teambuilding.