To definitely resolve whether this is an SDL problem or a Hatari problem, try installing SCUMMVM and a compatible game such as 'Beneath A Steel Sky' or 'Flight Of The Amazon Queen' - both available in the repos of most distros.
In fact I think if you install either of those games they will install SCUMMVM as a dependency, since both games need it to run.
Like Hatari, SCUMMVM uses SDL and has a fullscreen mode. If you have the cursor overspeed problem in fullscreen mode there as well, it's nothing to do with Hatari.
When I encountered this problem myself I jumped to the conclusion that it was a Hatari problem but it turned out to be an SDL problem, although only present for me in SDL1.2 - as you've already read, obtaining the source for and compiling SDL2 - which I had to do because SDL2 was not present in my old distro's repos - and then obtaining the (then) latest Hatari source and compiling it specifically for SDL2 using the --enable-sdl2 parameter fixed the problem for me.
When I say I compiled from the latest Hatari source, I mean a newer version than the current stable release V2.0.0. One of the devs will tell you shortly I'm sure, but I think something about the way Hatari renders the display has been changed during ongoing development of V2.x.x. Whether this will have any bearing on your problem remains to be seen.