Yes sorry I meant 1600, it's a little slower than the 1600X but not that much slower. I've used 1rst, 2nd and 3rd gen Ryzen for gaming and I've used Intel so I'm familiar with the performance of them but I've never actually played the games you mentioned. It does sound like they don't perform as well on Ryzen or at least that seems to be the case with Rust.
Unless I've missed something, your B350 doesn't support Zen 2 (Ryzen 3000). In terms of your options, if you can find a 2700X cheap anywhere then that would probably be a worthwhile improvement. Otherwise your looking at a new board and CPU, in which case at the price range your talking about then there aren't any worthwhile AMD options without spending more and moving to something like the 5600G.
I notice you say you have an 8700K, that's streets ahead of the 1600, that would fix your problem. That's slightly faster than the 10400F, but they are fundamentally the same thing. My only doubt is whether you can get a board for it at a reasonable price. I know here in the UK you can get a 10400F and a very good quality board for not that much money but it can be tricky with the older boards.
Can I ask what country you live in and what it is your max budget?