IMO, yes you'll have trouble with V-Rocker going down steeper slopes or ice. Think of your board as a swivel, or dredel spinning around in the middle. The V-Rocker offers tremendous "swiveling" ability while your on your board, but compromises edge hold and initiation.
Any board with raised edges (Bataleon 3D bases) or reserve-V cambers will have delayed grip or reduced grip compared to camber.
If you don't want to ride camber, but want to stay with some sort of hybrid camber, try looking for a board with slight reverse parabolic camber, such as the Banana tech or MtnPop rocker from Rome. These boards either have a mellower "U" shape, or a camber & rocker combo.
I had the Nitro Sub Pop which featured Gullwing rocker, an extreme version of the V-Rocker. I can totally understand the instability you talk about, especially on ice. I also had a Bataleon Goliath with Triple Base tech and edge initiation is definitely delayed, and sometimes in steep situations the edge grip just didn't cut it.
Get a board that has a combo of a flat section and/or camber with rocker, instead of purely V-Rocker.
Sharpening your edges won't help.