I think you can afford to take more risks than simply "play even safer in mid and hope things work out elsewhere." Trying something like this requires you to play more proactively than reactively - you need to look for opportunities to relieve pressure on bot, since you know (as you're the one running this strategy) that bot's going to be 1v2 and under constant pressure.
I personally think Tyler1, cuck that he is, managed to find a better answer than "play more defensively and pray" - he tried to roam. Mind you, in his game, he tried roaming bot, and it didn't work...I'll get to that in a moment, but I'm gonna start with Ashe, since you did.
With your example, Ashe honestly doesn't even really need to roam - just fire your ult from mid as your jungler sets up on a different lane, and you can more than likely net a very important release of enemy pressure, and/or get an assist or two. Bonus points if this works at bot, because you're still helping with the overall relevance of your late game damage dealer.
With Teemo, I imagine you have to be a little more creative since he's really not going to get anywhere near there without being noticed and collapsed on, but I could easily see a setup to bait the enemy to river by setting up shrooms and threatening dragon. At the very least, you're pushing objective control and you've already powerspiked your mid, so you have the stronger burst damage at this stage of the game. At best, you can set up a bit into enemy jungle, and perhaps get a catch as they try to get to dragon pit to place a ward. Both of these will pull some amount of attention from bot lane, as they're going to be paying constant attention to your encroachment around dragon/their jungle, and they're going to be looking to rotate if something starts to happen.
This is what I mean - he had at best a half-baked idea, and after funneling a lot of effort into spiking up mid's damage, he squandered it, and refused to change gears to make more proactive plays to keep the game alive. This happened in multiple games, not just this one.
We'll never really know in terms of the Nubrac/NB3 game, because everyone imploded around this crucial moment (read: I admit Nightblue refused to ever give this a solid chance once Sivir fell behind) but we know for a fact that even Irelia was asking for him to do something else, which he solidly refused to do. All the arguments caused by the confusion that he created derailed the game, and all the toxicity from Nightblue3 completely burned any hope of resetting it.