1) What would you do to try and turn things around the near term (1-6 months?)
I would improve the value proposition via bundling. I'd focus on strengths with regard to local multiplayer and the fact that there is free multiplayer. I'd announce a free retro game a month, the kind from back earlier consoles but not big name games.
I'd work hard to get a bunch of cell phone games ported over quickly to sell in the $3-5 range and thus increase appeal for parent types who are not hard core gamers. Things like the various Temple Run games Candy Crush, etc. This would also be part of addressing the third party strategy. If you change the nature of the third parties, then the conversation about support can shift. People don't need more Triple AAA titles demanding a season pass and starting at $60 to play. We have plenty and the ones that are out there want to come to Wii U anyway because they need to be everywhere to prove they are a franchise.
I'd work hard to improve the value proposition of the console within the bounds of the software available on it. Part of what made the Wii so fun was things like Everyone Votes, etc. You have to build habits. Apple gives away a free song of the week for example. People would check every Tuesday for it. Starbucks gives you stars and encourages consumption that way. People who do something daily on their Wii U are the best advocates for it and will talk it up to others. So give them 10% off online purchases for a length of time after X check in's or Y posts on MiiVerse or something along those lines. This sort of thing can be done quickly.
I'd work to bring more types of streaming channels and content to the WiiU. Again the apps here could be developed pretty quick and don't need lots of extra programming or horsepower.
2) Which device would you discontinue first (3DS/Wii U) and what would your timetable be for the transition of both devices?
I wouldn't discontinue either of those two. I would discontinue the Wii and clear out inventory on it. I wouldn't craft or create any new variants of it. I'd find everyone of them, pop in a couple older games and blow them out with two Wii-motes next Christmas for $100.
3) What would be the your strategy for bolstering 3rd party support on the next home console?
Again if you can't win with the current equation, change the game. Bring a bunch of inexpensive cell games in for cheap and take a cut from the sales. I'd also go to all the free to play PC games and offer some cash for them to port their games over to Wii U. Finally do whatever it takes to get Minecraft onto the WiiU and 3ds.