Steep and deep, leads me to lean towards the 2016 LT. I would get the TSS fit kit to help with being aggressive. I would think the yeti would perform well for what you are doing, but a bit more money. You could also get a used LT dirt cheap and install a new timbersled or C3 track.
As for bike if you want an affordable good performing machine, yz450f, relatively light and good power. There are several good choices for KTM machines if you want Estart etc.
If you want to keep the budget down and have even more hill shredding power get a cr500 and prepare to install a few mods, still cheaper.
If you want to spend 20k total you could have an insane climbing machine with a turbo.
I'll fill you in on what I am doing and why. I'm rebuilding my cr500 and converting it to an aluminum frame. Picking up a '16 sx120 with tss. I like climbing but I know it would be hard to replicate on a bike what sleds can do, but it's getting closer to being possible. So instead I am going for something that will be extremely light maneuverable, jump and do drops well, handle trees, but might suffer slightly on the deep with the much less flotation and the track angle of the sx. I want the short track so I don't have as much hanging up off the back when jumping or dropping. So in essence I'll get smoked by some of the guys I will be riding with since they will be doing serious climbs but I should get around to anywhere just as well or better, the hills and poweder will be a bit more of a challenge. With that said, I have no experience on a snow bike....