You are correct in your assumption that the cut-away faces the rear of the bike and that this is for more air.
The cut-away only affects air-flow at small throttle openings, this is when air flow is at its lowest and needs a bit of assistance.
It is strange that everything works perfectly with the slides the wrong way round, so to answer your Q, you won't hurt anything with the slides the wrong way round, but you have definetely not fixed your original problem, just covered it up.
What are your mods, elevation and ambient conditions? Also let us know all your carb settings, pilot size, main jet size, needle clip position etc.