I think the $120 might be worth it, but I'm not sure going a lot above that would be. TPU's 9700K review has your i3-8350K and the 8700K listed in it so that'd be worth skimming through to see if you're likely to see a benefit for what you do.
Intel's Core i7-9700K comes with eight cores, but lacks HyperThreading. In our testing, it still conclusively beats the 6-core/12-thread Core i7-8700K. The much more expensive Core i9-9900K is also under heavy attack: it seems the Core i7-9700K actually is the better gaming CPU.
www.techpowerup.com
At some point you're going to be spending more money on an old platform than it's worth and the entry price for LGA1700 with a 12400F is about $270 with motherboard and cooler.