The online community for MiSTer FPGA enthusiasts
https://misterfpga.org/
Is anyone else having problems with the left side of the screen of King of Monsters, where you can see the background tiles being added to the screen with still black parts of the screen under those tiles? So there is no smooth scrolling. Is this part of the screen supposed to be covered up by a black border?
KotM is one of the 304px games...
https://www.patreon.com/posts/neo-geo-320-vs-90490687
You can change it in the video options.
However, scrolling is a lot smoother on original hardware (even though it scrolls in chunks). Seems to be MiSTer specific.
I just checked this on my MV1C and can't see any difference in the scrolling, either on a CRT or through a RetroTink 5x. Have you tried an alternative vsync_adjust setting on your display?
Failing that, I can't see any open issues on the Neo Geo core's GitHub. It would be worth raising it there too see if it can be reproduced.
Scrolling is fine on CRTs (of course). This is the way those games should be played anyway. 
However. I did some more testing with AES hardware and scalers.
It looks like the RetroTink 5x Pro is able to handle the (odd) scrolling of KotM, with Horizontal Sampling > Preset > NEOGEO 320. There's no "scroll jumping" at the edges, it looks like on a CRT.
The RT5x generic 4:3 preset and my other scalers (Framemeister & OSSC) scroll the same (odd) way as the MiSTer does.
So it's not a MiSTer problem, rather a RetroTink 5x Pro feature. 
Have you compared the performance with any other Neo Geo games to see if it's specific to King of Monsters?
I don't think it's a matter of performance, just the (odd) way how scrolling was implemented for KotM. Don't know which other NG games have similar scrolling issues, since I mostly play them on CRTs.
The RT5x is able to compensate this specific scrolling behaviour. I don't know how this technically works. But I would like to know, if the behavior on a RT4K is the same as on RT5x. Maybe someone with both scalers can test it.