Masked materials display as opaque in reflections

So, I have created a shader that makes use of masked materials. The idea is that it cuts out chunks of the scenery in order to display the player when they would be obscured by foreground elements. This works quite nicely, and using various tricks I can maintain the shadows for the entire object.

What I don’t seem to be able to do, however, is maintain the entire object for reflections, without the mask applied. I understand that this isn’t possible with screen space reflections because of how those work, and that’s fine, but I don’t seem to be able to manage any settings with reflection captures, either. I don’t even seem to be able to hide the object to the reflection capture and display a separate one only to that.

Is this something I can do? Are reflection captures at all customisable?