Suggestions for building a lens system for 6D

I have had a 6D for about 2.5 years and I use it with the 16-35f/4is, 24-105f/4 (from 6D kit), 70-200f/2.8isII, 50f/1.8STM, 35f/2IS.

My $0.02 on what you should get:
16-35
24-105
100-400 MkII
plus the 50f/1.8STM you already have

16-35f/4 is fantastic, as everyone says. Your use case sounds perfect for it.

For the telephoto, I adore my 70-200 and I use it for hiking, landscapes and nature but I got it more for people/events and just because it made me happy. The f/4 version is just as good (minus the 2.8) and smaller/cheaper. But I find that 200 isn't long enough sometimes. The 70-300L and the 100-400II are both reported to be fantastic - get the 70-300 if travelling size is an issue (it's shorter and fits in bags easier, and I think it's a better travel option than 70-200f/4+1.4X) otherwise get the 100-400.  Any of the four are great though.

I'd still recommend getting the 24-105f/4 at some point. It may not be the most critically sharp lens (although mine is very good after MFA) but it is durable, handles well and has a good range with IS. It is perfect for when you want to go out with just one lens. It's unfortunate you didn't pick it up as a kit but you can find white-box versions pulled out of kits for a reasonable price.  But for a start you could carry the 16-35 and 70/100 telephoto plus your 50mm and have a reasonable compact 3-lens set.

So, 1) yes it's a good shortlist, 2) I'd get the 16-35 if you had to pick but I don't see them as an either/or option, 3) I have no experience with Tamron/Sigma.

Good luck.