Wouldn't you be aiming to keep vram usage below 4GB on a 4GB card?
Whether through drivers or through developer choices based on detected video memory (this is a DX12 game, right?), I would have though you'd be trying to do exactly that. And it wouldn't necessarily mean it wasn't costing you performance.
Store what you need to in main memory, and transfer only as much into video memory as you can fit and stream as appropriate, even if there's overhead to that.
Whether through drivers or through developer choices based on detected video memory (this is a DX12 game, right?), I would have though you'd be trying to do exactly that. And it wouldn't necessarily mean it wasn't costing you performance.
Store what you need to in main memory, and transfer only as much into video memory as you can fit and stream as appropriate, even if there's overhead to that.