Not much loss in stacking as long as the paste is used correctly. Not ideal but not bad.
Regular thermal paste is very thin once applied and meant to only fill in tiny gaps such as slight machining marks and very minor surface flatness issues. Not even a single thickness of notebook paper should be involved. And any reputable brand will do- I'm still using an old tube of cheap crap from Radio Shack I got ten years ago. You don't need much but it needs to be applied everywhere there should be contact. And paste joints need parts clamping for use- they aren't meant to hold or align parts. Anything thicker will have more heat-transfer losses, and if you can't do clamping that's what thermal epoxy is for, not paste.
Only geeks pushing their PC's to insane levels need to be particular about which paste to use. With something like this even my cheap paste won't be bested by more than a degree or two of cam operating temp by the very best pastes, and maybe not even that much. This is "proof of concept" work, so all you need is to show that the improved heat sinking actually does work well, and you or Zenfox can fine-tune everything later to get that last degree.
Phil