I occasionally run the latest version of JJ2+ on my work MacBook through Wine (a recent OS X build) and haven't encountered any wrongful behavior compared to native Windows. Maybe Wine's even better, as both my gaming PC's are running Windows 10 with Nvidia drivers that still like to mess up DDraw to stutter, while I had Wine set to be like XP (which gives me a smoother, 60fps capped fullscreen somehow).

Anyhow, using a recent build of Wine seems to be a good idea, at least.