This warps the reflection lookup vectors? Interesting.
The sphere versus box difference in Unreal has to do with how the texture is stored (spherical versus cube map projection,) but not how the reflection texture lookup is done as far as I know.
If you want reflections that work “right” along a wall, you can use a planar reflection capture (need to turn on clipping plane support) but that’s not a low-cost solution if you need six of them. Of course, if you don’t have that much geometry, it might be perfectly fine – you could try!
The other solution is ray tracing. Mobile VR will do that next generation, so depending on how long your projected project development time is, maybe that’s an option 